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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
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
Journal Article
Results in Mathematics, ISSN 1422-6383, 9/2018, Volume 73, Issue 3, pp. 1 - 46
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
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
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
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 7/2018, Volume 28, Issue 3, pp. 2670 - 2691
Journal Article
TOKYO JOURNAL OF MATHEMATICS, ISSN 0387-3870, 12/2017, Volume 40, Issue 2, pp. 301 - 337
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
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
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
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
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
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
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
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 1/2012, Volume 61, Issue 2, pp. 831 - 847
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
Journal Article
Annals of Global Analysis and Geometry, ISSN 0232-704X, 1/2013, Volume 43, Issue 1, pp. 47 - 62
Journal Article
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