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International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 09/2018, Volume 15, Issue 9
The present paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as... 
Generalized Sasakian-space-forms | Ricci soliton | totally geodesic | invariant submanifold | semi-symmetric metric connection | semi parallel submanifold | Mathematics - Differential Geometry
Journal Article
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
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 1, pp. 488 - 498
We deal with complete submanifolds Mn having constant positive scalar curvature and immersed with parallel normalized mean curvature vector field in a... 
Circular and hyperbolic cylinders | Clifford torus | Parallel normalized mean curvature vector field | Constant normalized scalar curvature | Riemannian space forms | Complete submanifolds | MATHEMATICS | MATHEMATICS, APPLIED | HYPERSURFACES | SPHERE | MEAN-CURVATURE | RIEMANNIAN-MANIFOLDS
Journal Article
2003, ISBN 9789812386878, viii, 262
Book
Journal of Differential Geometry, ISSN 0022-040X, 10/2016, Volume 104, Issue 2, pp. 187 - 217
Let M be an irreducible Riemannian symmetric space. The index i(M) of M is the minimal codimension of a totally geodesic submanifold of M. In [1] we proved... 
MATHEMATICS | COMPLEX
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2009, Volume 56, Issue 1, pp. 231 - 244
Parallel submanifolds are studied in cases of submanifolds of arbitrary codimension, hypersurfaces and Lagrangian submanifolds. 
53C42 | Parallel submanifolds | 53A15 | Lagrangian submanifold | Mathematics, general | Mathematics | 53B05 | congruent submanifolds | Blaschke structure | Congruent submanifolds | MATHEMATICS | MATHEMATICS, APPLIED | REAL-SUBMANIFOLDS | AFFINE GEOMETRY
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
Journal of Geometry and Physics, ISSN 0393-0440, 06/2016, Volume 104, pp. 163 - 174
In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with... 
Parallel submanifolds | Wick-related spaces | Anti-Kähler geometry | Complex and holomorphic Riemannian geometry | Minimal submanifolds | Mathematics - Differential Geometry
Journal Article
Science China Mathematics, ISSN 1674-7283, 4/2017, Volume 60, Issue 4, pp. 671 - 684
We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Kähler manifold are totally geodesic. Moreover, under some weaker conditions, a... 
isotropic submanifold | 53C42 | totally geodesic | 53C30 | nearly Kähler S 3 ×S 3 | 53D12 | 53B35 | Lagrangian submanifold | Mathematics | Applications of Mathematics | J -parallel | J-parallel | nearly Kähler S
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 1/2013, Volume 62, Issue 4, pp. 1283 - 1314
We give a complete classification of submanifolds with parallel second fundamental form of a product of two space forms. We also address the classification of... 
Tangents | Tensors | Riemann manifold | Vector fields | Hypersurfaces | Mathematical vectors | Curvature | Unit vectors | Normal spaces | Parallel submanifolds | Products of space forms | Umbilical submanifolds | Reduction of codimension | MATHEMATICS | umbilical submanifolds | reduction of codimension | products of space forms | ISOMETRIC IMMERSIONS | PARALLEL
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
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 7/2019, Volume 42, Issue 4, pp. 1469 - 1484
In this paper, we investigate biharmonic submanifolds with parallel normalized mean curvature vector field in pseudo-Riemannian space forms and classify... 
53C50 | Mathematics, general | Mathematics | Applications of Mathematics | Parallel normalized mean curvature vector field | Pseudo-Riemannian space forms | Biharmonic submanifolds | MATHEMATICS
Journal Article
Indian Journal of Mathematics, ISSN 0019-5324, 12/2017, Volume 59, Issue 3, pp. 385 - 402
Journal Article
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, ISSN 0219-8878, 04/2019, Volume 16, Issue 4
We study complete linear Weingarten spacelike submanifolds with arbitrary high codimension p in the de Sitter space S-P(n+p) of index p and whose normalized... 
CONSTANT MEAN-CURVATURE | De Sitter space | hyperbolic cylinders | HYPERSURFACES | parallel normalized mean curvature vector | PHYSICS, MATHEMATICAL | spacelike submanifolds | complete linear Weingarten submanifolds | VECTOR | SURFACES
Journal Article
Journal Article
Axioms, ISSN 2075-1680, 10/2019, Volume 8, Issue 4, p. 120
A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der... 
thurston 3d geometries | complex space form | kaehler submanifolds | parallel submanifold | real space form | totally real submanifolds | bianchi–cartan–vranceasu spaces | light cone
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
Mediterranean Journal of Mathematics, ISSN 1660-5446, 2/2018, Volume 15, Issue 1, pp. 1 - 22
In this paper, we deal with complete spacelike submanifolds $$M^n$$ Mn immersed in the de Sitter space $$\mathbb S_p^{n+p}$$ Spn+p of index p with parallel... 
53C20 | Primary 53C42 | De Sitter space | 53C50 | hyperbolic cylinders | constant scalar curvature | parallel normalized mean curvature vector | Mathematics, general | Secondary 53A10 | Mathematics | totally umbilical submanifolds | MATHEMATICS, APPLIED | SPHERES | VECTOR | MATHEMATICS | DESITTER SPACE | HYPERSURFACES | MEAN-CURVATURE | RIEMANNIAN-MANIFOLDS
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2016, Volume 18, Issue 6, p. 1550073
In this paper, our aim is to study the geometry of n -dimensional trapped and marginally trapped submanifolds immersed in a Lorentzian space form L 1 n + p ( c... 
parallel mean curvature vector | marginally trapped submanifolds | trapped submanifolds | Lorentzian space forms | totally umbilical submanifolds | MATHEMATICS, APPLIED | GRAVITATIONAL COLLAPSE | SINGULARITIES | COMPLETE CLASSIFICATION | MEAN-CURVATURE VECTOR | MATHEMATICS | HYPERSURFACES | SURFACES
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
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