2003, Research notes in mathematics, ISBN 1584883715, Volume 434., 336

With special emphasis on new techniques based on the holonomy of the normal connection, this book provides a modern, self-contained introduction to submanifold...

Holonomy groups | Submanifolds | Riemannian manifolds | isoparametric submanifolds | STMnetBASE | Moore’s lemma for local splitting | SCI-TECHnetBASE | MATHnetBASE | holonomy of complex submanifolds | Berger–Simons holonomy theorem | geodesic submanifolds | skew-torsion holonomy system | Geometry | normal holonomy theorem | polar actions on symmetric spaces | submanifold geometry of space forms | geometry of submanifolds | orbits for isometric actions | Number Theory | homogeneous submanifolds

Holonomy groups | Submanifolds | Riemannian manifolds | isoparametric submanifolds | STMnetBASE | Moore’s lemma for local splitting | SCI-TECHnetBASE | MATHnetBASE | holonomy of complex submanifolds | Berger–Simons holonomy theorem | geodesic submanifolds | skew-torsion holonomy system | Geometry | normal holonomy theorem | polar actions on symmetric spaces | submanifold geometry of space forms | geometry of submanifolds | orbits for isometric actions | Number Theory | homogeneous submanifolds

Book

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 6/2019, Volume 60, Issue 2, pp. 339 - 349

We use suitable maximum principles in order to obtain characterization results concerning n-dimensional linear Weingarten submanifolds immersed with globally...

53C20 | Primary 53C42 | 53C50 | Mathematics | Isoparametric submanifolds | Hyperbolic space | Geometry | Algebra | Convex and Discrete Geometry | Algebraic Geometry | Secondary 53A10 | Parallel normalized mean curvature vector field | Complete linear Weingarten submanifolds

53C20 | Primary 53C42 | 53C50 | Mathematics | Isoparametric submanifolds | Hyperbolic space | Geometry | Algebra | Convex and Discrete Geometry | Algebraic Geometry | Secondary 53A10 | Parallel normalized mean curvature vector field | Complete linear Weingarten submanifolds

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 9, pp. 1549 - 1560

Let E be a simply connected rational homology sphere. A pair of disjoint closed submanifolds M＋, M_ C ＋ are called dual to each other if the complement ~ - M＋...

Dupin超曲面 | 有理 | simple | vector | 微分同胚 | Cartan | 同调 | 闭子流形 | dual submanifold | rational homology sphere | 55P62 | Mathematics | Applications of Mathematics | cohomogeneity one action | isoparametric hypersurface | 57N65 | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | ISOPARAMETRIC HYPERSURFACES | DUPIN HYPERSURFACES | MULTIPLICITIES

Dupin超曲面 | 有理 | simple | vector | 微分同胚 | Cartan | 同调 | 闭子流形 | dual submanifold | rational homology sphere | 55P62 | Mathematics | Applications of Mathematics | cohomogeneity one action | isoparametric hypersurface | 57N65 | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | ISOPARAMETRIC HYPERSURFACES | DUPIN HYPERSURFACES | MULTIPLICITIES

Journal Article

Results in Mathematics, ISSN 1422-6383, 9/2018, Volume 73, Issue 3, pp. 1 - 46

In this paper, we establish a complete classification of umbilic-free submanifolds of the unit sphere with parallel Möbius second fundamental form and...

Secondary 53B25 | Primary 53A30 | umbilic-free submanifold | Blaschke tensor | parallel submanifold | Mathematics, general | Mathematics | Möbius second fundamental form | MATHEMATICS, APPLIED | Mobius second fundamental form | DISTINCT PRINCIPAL CURVATURES | SPACE FORMS | ISOPARAMETRIC HYPERSURFACES | CLASSIFICATION | SCALAR CURVATURE | SYMMETRIC SUB-MANIFOLDS | MATHEMATICS | S-N | MEAN-CURVATURE | GEOMETRY

Secondary 53B25 | Primary 53A30 | umbilic-free submanifold | Blaschke tensor | parallel submanifold | Mathematics, general | Mathematics | Möbius second fundamental form | MATHEMATICS, APPLIED | Mobius second fundamental form | DISTINCT PRINCIPAL CURVATURES | SPACE FORMS | ISOPARAMETRIC HYPERSURFACES | CLASSIFICATION | SCALAR CURVATURE | SYMMETRIC SUB-MANIFOLDS | MATHEMATICS | S-N | MEAN-CURVATURE | GEOMETRY

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 3/2018, Volume 53, Issue 2, pp. 205 - 216

We show that an isoparametric submanifold of a complex hyperbolic plane, according to the definition of Heintze, Liu and Olmos’, is an open part of a principal...

53C40 | 53C35 | 53C12 | Theoretical, Mathematical and Computational Physics | Complex projective plane | Isoparametric submanifold | Mathematics | Polar action | Geometry | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | principal curvatures | Complex hyperbolic plane | Group Theory and Generalizations | MATHEMATICS | CONSTANT PRINCIPAL CURVATURES | FOLIATIONS | REAL HYPERSURFACES | Needlework | Manifolds (mathematics)

53C40 | 53C35 | 53C12 | Theoretical, Mathematical and Computational Physics | Complex projective plane | Isoparametric submanifold | Mathematics | Polar action | Geometry | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | principal curvatures | Complex hyperbolic plane | Group Theory and Generalizations | MATHEMATICS | CONSTANT PRINCIPAL CURVATURES | FOLIATIONS | REAL HYPERSURFACES | Needlework | Manifolds (mathematics)

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2015, Volume 67, Issue 3, pp. 903 - 942

It was conjectured, twenty years ago, the following result that would generalize the so-called rank rigidity theorem for homogeneous Euclidean submanifolds:...

Orbits of s-representations | Veronese submanifolds | Normal holonomy | POLAR REPRESENTATIONS | PARALLEL MEAN-CURVATURE | THEOREM | SPACES | HIGHER RANK | MATHEMATICS | ISOPARAMETRIC SUBMANIFOLDS | S-REPRESENTATIONS | normal holonomy | IMMERSIONS | MANIFOLDS | orbits of s-representations

Orbits of s-representations | Veronese submanifolds | Normal holonomy | POLAR REPRESENTATIONS | PARALLEL MEAN-CURVATURE | THEOREM | SPACES | HIGHER RANK | MATHEMATICS | ISOPARAMETRIC SUBMANIFOLDS | S-REPRESENTATIONS | normal holonomy | IMMERSIONS | MANIFOLDS | orbits of s-representations

Journal Article

Forum Mathematicum, ISSN 0933-7741, 07/2015, Volume 27, Issue 4, pp. 2467 - 2490

We introduce a new class of submanifolds of co-Banach type in tame Fréchet manifolds and construct tame Fréchet submanifolds as inverse images of regular...

tame Fréchet submanifold | Kac–Moody geometry | 58B25 | 58B99 | isoparametric submanifold | 22E67 | manifold of co-Banach type | implicit function theorem | Kac-Moody geometry | MATHEMATICS | MATHEMATICS, APPLIED | INVERSE FUNCTION THEOREM | SPACES | SMOOTH | IMPLICIT FUNCTIONS | tame Frechet submanifold | NASH

tame Fréchet submanifold | Kac–Moody geometry | 58B25 | 58B99 | isoparametric submanifold | 22E67 | manifold of co-Banach type | implicit function theorem | Kac-Moody geometry | MATHEMATICS | MATHEMATICS, APPLIED | INVERSE FUNCTION THEOREM | SPACES | SMOOTH | IMPLICIT FUNCTIONS | tame Frechet submanifold | NASH

Journal Article

Science China Mathematics, ISSN 1674-7283, 07/2017, Volume 60, Issue 7, pp. 1281 - 1310

The Blaschke tensor and the Mobius form are two of the fundamental invariants in the Mobius geometry of submanifolds; an umbilic-free immersed submanifold in...

parallel mean curvature vector | parallel Blaschke tensor | constant scalar curvature | vanishing Möbius form | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | vanishing Mobius form | SM+1 | ISOPARAMETRIC HYPERSURFACES | SCALAR CURVATURE | IMMERSED HYPERSURFACES | UNIT-SPHERE | MATHEMATICS | S-N | MEAN-CURVATURE | GEOMETRY

parallel mean curvature vector | parallel Blaschke tensor | constant scalar curvature | vanishing Möbius form | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | vanishing Mobius form | SM+1 | ISOPARAMETRIC HYPERSURFACES | SCALAR CURVATURE | IMMERSED HYPERSURFACES | UNIT-SPHERE | MATHEMATICS | S-N | MEAN-CURVATURE | GEOMETRY

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 7/2018, Volume 28, Issue 3, pp. 2670 - 2691

The conformal geometry of submanifolds in a constant curvature space was well studied in the past 15 years. The first part of this paper presents the system of...

Integral inequality | 53C40 | 53A30 | 53C21 | Mathematics | Abstract Harmonic Analysis | Willmore tori | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Submanifolds | Conformal invariant | MATHEMATICS | MOBIUS ISOPARAMETRIC HYPERSURFACES | DISTINCT PRINCIPAL CURVATURES | FORM | SM+1 | MEAN-CURVATURE | CLASSIFICATION | GEOMETRY

Integral inequality | 53C40 | 53A30 | 53C21 | Mathematics | Abstract Harmonic Analysis | Willmore tori | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Submanifolds | Conformal invariant | MATHEMATICS | MOBIUS ISOPARAMETRIC HYPERSURFACES | DISTINCT PRINCIPAL CURVATURES | FORM | SM+1 | MEAN-CURVATURE | CLASSIFICATION | GEOMETRY

Journal Article

TOKYO JOURNAL OF MATHEMATICS, ISSN 0387-3870, 12/2017, Volume 40, Issue 2, pp. 301 - 337

In this paper, we prove that, if a full irreducible infinite dimensional anti-Kaehler isoparametric submanifold of codimension greater than one has...

SPLITTING THEOREM | REPRESENTATIONS | J-curvature distribution | MATHEMATICS | homogeneous structure | holomorphic Killing vector field | J-principal curvature | SEMISIMPLE SYMMETRIC-SPACES | COMPLEXIFICATION | anti-Kaehler isoparametric submanifold | HILBERT-SPACE | COMPLEX EQUIFOCAL SUBMANIFOLDS | GEOMETRY | Mathematics - Differential Geometry

SPLITTING THEOREM | REPRESENTATIONS | J-curvature distribution | MATHEMATICS | homogeneous structure | holomorphic Killing vector field | J-principal curvature | SEMISIMPLE SYMMETRIC-SPACES | COMPLEXIFICATION | anti-Kaehler isoparametric submanifold | HILBERT-SPACE | COMPLEX EQUIFOCAL SUBMANIFOLDS | GEOMETRY | Mathematics - Differential Geometry

Journal Article

数学学报：英文版, ISSN 1439-8516, 2015, Volume 31, Issue 12, pp. 1963 - 1969

In this paper,we show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore,hence...

函数 | 主曲率 | 子流形 | 单位球面 | 等参超曲面 | 球体 | focal submanifold | 53C42 | 53A30 | Mathematics, general | Mathematics | soparametric hypersurface | Willmore submanifold | MATHEMATICS | MATHEMATICS, APPLIED | HYPERSURFACES | FOLIATION | 1ST EIGENVALUE | 4 PRINCIPAL CURVATURES | YAU CONJECTURE | isoparametric hypersurface | Studies | Mathematical models

函数 | 主曲率 | 子流形 | 单位球面 | 等参超曲面 | 球体 | focal submanifold | 53C42 | 53A30 | Mathematics, general | Mathematics | soparametric hypersurface | Willmore submanifold | MATHEMATICS | MATHEMATICS, APPLIED | HYPERSURFACES | FOLIATION | 1ST EIGENVALUE | 4 PRINCIPAL CURVATURES | YAU CONJECTURE | isoparametric hypersurface | Studies | Mathematical models

Journal Article

Results in Mathematics, ISSN 1422-6383, 9/2016, Volume 70, Issue 1, pp. 183 - 195

The focal submanifolds of isoparametric hypersurfaces in spheres are all minimal Willmore submanifolds, mostly being $${\mathcal{A}}$$ A -manifolds in the...

53C42 | focal submanifold | 53A30 | semiparallel | Mathematics, general | Mathematics | Isoparametric hypersurface | normally flat | MATHEMATICS | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | SPHERES | CONJECTURE

53C42 | focal submanifold | 53A30 | semiparallel | Mathematics, general | Mathematics | Isoparametric hypersurface | normally flat | MATHEMATICS | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | SPHERES | CONJECTURE

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2015, Volume 58, Issue 8, pp. 1723 - 1736

A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci...

主曲率 | 张量 | 子流形 | 爱因斯坦流形 | 等参超曲面 | 单位球面 | 黎曼流形 | focal submanifold | 53C42 | 53A30 | Mathematics | B -manifold | Applications of Mathematics | isoparametric hypersurface | A -manifold | A-manifold | B-manifold | MATHEMATICS | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES

主曲率 | 张量 | 子流形 | 爱因斯坦流形 | 等参超曲面 | 单位球面 | 黎曼流形 | focal submanifold | 53C42 | 53A30 | Mathematics | B -manifold | Applications of Mathematics | isoparametric hypersurface | A -manifold | A-manifold | B-manifold | MATHEMATICS | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES

Journal Article

Advances in Geometry, ISSN 1615-715X, 04/2016, Volume 16, Issue 2, pp. 243 - 251

Chen and Lue (2007) initiated the study of spherical submanifolds with finite type spherical Gauss map. In this paper, we firstly prove that a submanifold M of...

spherical Gauss map | isoparametric hypersurface | Finite type map | mean curvature | MATHEMATICS

spherical Gauss map | isoparametric hypersurface | Finite type map | mean curvature | MATHEMATICS

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 02/2015, Volume 26, Issue 2, pp. 1550014 - 1-1550014-18

We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss...

hyperbolic Gauss map | isoparametric hypersurfaces | Finite type map | horohypersphere | mean curvature | biharmonic map | MATHEMATICS | Geometry | Mathematical analysis | Classification | Scalars | Constants | Manifolds (mathematics) | Curvature | Manganese

hyperbolic Gauss map | isoparametric hypersurfaces | Finite type map | horohypersphere | mean curvature | biharmonic map | MATHEMATICS | Geometry | Mathematical analysis | Classification | Scalars | Constants | Manifolds (mathematics) | Curvature | Manganese

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 12/2014, Volume 37, pp. 89 - 108

Let N be a complex flag manifold of a compact semi-simple Lie group G, which is standardly embedded in the Lie algebra g of G as a principal orbit of the...

Hamiltonian minimal Lagrangian submanifolds | Complex flag manifolds | Isoparametric submanifolds | Normal bundles | MATHEMATICS | MATHEMATICS, APPLIED | LAGRANGIAN SUBMANIFOLDS | HYPERSURFACES | SPHERES | Algebra

Hamiltonian minimal Lagrangian submanifolds | Complex flag manifolds | Isoparametric submanifolds | Normal bundles | MATHEMATICS | MATHEMATICS, APPLIED | LAGRANGIAN SUBMANIFOLDS | HYPERSURFACES | SPHERES | Algebra

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 06/2014, Volume 25, Issue 6, pp. 1450062 - 1-1450062-37

In this paper, we study umbilic-free submanifolds of the unit sphere with parallel Möbius second fundamental form. As one of our main results, we establish a...

Umbilic-free | Parallel submanifold | Möbius second fundamental form | Blaschke tensor | Mobius second fundamental form | DISTINCT PRINCIPAL CURVATURES | ISOPARAMETRIC HYPERSURFACES | CLASSIFICATION | SYMMETRIC SUB-MANIFOLDS | SPACE | MATHEMATICS | umbilic-free | S-N | parallel submanifold | IMMERSIONS | CODIMENSION-2 | GEOMETRY | Mathematical analysis | Mathematics | Classification

Umbilic-free | Parallel submanifold | Möbius second fundamental form | Blaschke tensor | Mobius second fundamental form | DISTINCT PRINCIPAL CURVATURES | ISOPARAMETRIC HYPERSURFACES | CLASSIFICATION | SYMMETRIC SUB-MANIFOLDS | SPACE | MATHEMATICS | umbilic-free | S-N | parallel submanifold | IMMERSIONS | CODIMENSION-2 | GEOMETRY | Mathematical analysis | Mathematics | Classification

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2012, Volume 61, Issue 2, pp. 831 - 847

Curvature-adapted submanifolds have been extensively studied in complex and quaternionic space forms. This paper extends their study to a wider class of...

Geometry | Riemann manifold | Geometric planes | Hypersurfaces | Eigenvalues | Mathematical constants | Riccati equation | Curvature | Symmetry | Complex two-plane Grassmannians | Curvature-adapted hypersurfaces | Cayley projective and hyperbolic planes | Isoparametric hypersurfaces | MATHEMATICS | FORM | COMPLEX PROJECTIVE-SPACE | curvature-adapted hypersurfaces | isoparametric hypersurfaces | complex two-plane Grassmannians | REAL HYPERSURFACES

Geometry | Riemann manifold | Geometric planes | Hypersurfaces | Eigenvalues | Mathematical constants | Riccati equation | Curvature | Symmetry | Complex two-plane Grassmannians | Curvature-adapted hypersurfaces | Cayley projective and hyperbolic planes | Isoparametric hypersurfaces | MATHEMATICS | FORM | COMPLEX PROJECTIVE-SPACE | curvature-adapted hypersurfaces | isoparametric hypersurfaces | complex two-plane Grassmannians | REAL HYPERSURFACES

Journal Article

Mathematische Annalen, ISSN 0025-5831, 9/2011, Volume 351, Issue 1, pp. 187 - 214

We prove a Berger type theorem for the normal holonomy $${\Phi^\perp}$$ (i.e., the holonomy group of the normal connection) of a full complete complex...

Primary 53C30 | Mathematics, general | Mathematics | Secondary 53C21 | MATHEMATICS | ISOPARAMETRIC SUBMANIFOLDS | HIGHER RANK | PARALLEL MEAN-CURVATURE | PROJECTIVE-SPACE

Primary 53C30 | Mathematics, general | Mathematics | Secondary 53C21 | MATHEMATICS | ISOPARAMETRIC SUBMANIFOLDS | HIGHER RANK | PARALLEL MEAN-CURVATURE | PROJECTIVE-SPACE

Journal Article

20.
Full Text
New examples of Willmore submanifolds in the unit sphere via isoparametric functions, II

Annals of Global Analysis and Geometry, ISSN 0232-704X, 1/2013, Volume 43, Issue 1, pp. 47 - 62

This paper is a continuation and wide extension of (Ann. Glob. Anal. Geom., doi: 10.1007/s10455-012-9319-z , 2012). In the first part of the present paper, we...

Geometry | 53C42 | 53A30 | Focal submanifolds | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Group Theory and Generalizations | Isoparametric functions | Willmore submanifold | MATHEMATICS | 4 PRINCIPAL CURVATURES | HYPERSURFACES | Studies | Topological manifolds | Mathematical analysis | Curvature | Proving | Mathematics - Differential Geometry

Geometry | 53C42 | 53A30 | Focal submanifolds | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Group Theory and Generalizations | Isoparametric functions | Willmore submanifold | MATHEMATICS | 4 PRINCIPAL CURVATURES | HYPERSURFACES | Studies | Topological manifolds | Mathematical analysis | Curvature | Proving | Mathematics - Differential Geometry

Journal Article

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