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Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2019, Volume 147, Issue 12, pp. 5417 - 5420
In this note we construct an explicit example of a (compact) conformally flat Riemannian manifold which admits a totally geodesic foliation of codimension one... 
MATHEMATICS | MATHEMATICS, APPLIED | Isoparametric hypersurface | constant principal curvatures
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 2018, Volume 146, Issue 11, pp. 4867 - 4878
It is shown that a hypersurface of a space form is the initial data for a solution to the mean curvature flow by parallel hypersurfaces if and only if it is... 
Parallel hypersurface | Isoparametric hypersurface | And phrases | Mean curvature flow | Space forms | MATHEMATICS | MATHEMATICS, APPLIED | parallel hypersurface | PRINCIPAL CURVATURES | space forms | ISOPARAMETRIC HYPERSURFACES | mean curvature flow
Journal Article
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 08/2016, Volume 47, pp. 133 - 158
In this paper, we introduce isoparametric functions and isoparametric hypersurfaces in Finsler manifolds and give the necessary and sufficient conditions for a... 
Finsler–Laplacian | Principal curvature | Isoparametric function | Mean curvature | Isoparametric hypersurfaces | Secondary | Primary | Finsler-Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | 1ST EIGENVALUE | FINSLER MANIFOLDS | Computer science | Hyperspheres | Geometry | Mathematical analysis | Classification | Minkowski space | Constants | Manifolds (mathematics) | Cylinders
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 12, pp. 2447 - 2464
Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in... 
34D23 | principal curvature | Funk metric | Mathematics | Applications of Mathematics | Finsler-Laplacian | isoparametric hypersurfaces | 53C60 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2018, Volume 70, Issue 2, pp. 463 - 480
Similar to the definition in Riemannian space forms, we define the spacelike Dupin hypersurface in Lorentzian space forms. As conformal invariant objects,... 
Dupin hypersurface | Principal curvatures | Möbius curvatures | Conformal isoparametric hypersurface | conformal isoparametric hypersurface | MATHEMATICS | 3 PRINCIPAL CURVATURES | principal curvatures | ISOPARAMETRIC HYPERSURFACES | Mobius curvatures
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 12/2010, Volume 283, Issue 12, pp. 1696 - 1705
We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper... 
Biharmonic submanifolds, principal curvatures, isoparametric hypersurfaces | MATHEMATICS | SUBMANIFOLDS | principal curvatures | SPHERES | CURVATURE VECTOR | isoparametric hypersurfaces | Biharmonic submanifolds
Journal Article
Advances in Mathematics, ISSN 0001-8708, 06/2013, Volume 239, pp. 1 - 17
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 10/2016, Volume 48, Issue 5, pp. 802 - 812
Abstract In this article, we study the Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces in the spheres as Lagrangian submanifolds... 
MATHEMATICS | LAGRANGIAN SUBMANIFOLDS | STABILITY
Journal Article
Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 6/2018, Volume 197, Issue 3, pp. 703 - 720
In this paper, I study the isoparametric hypersurfaces in a Randers sphere $$(S^n,F)$$ (Sn,F) of constant flag curvature, with the navigation datum (h, W). I... 
53C42 | Navigation | Randers sphere of constant flag curvature | Mathematics, general | Mathematics | Isoparametric function | Isoparametric hypersurface | 53C60 | Homogeneous hypersurface | 22E46 | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | FAMILIES | 4 PRINCIPAL CURVATURES | RIEMANNIAN-MANIFOLDS
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2018, Volume 15, Issue 6, pp. 1 - 14
In this paper, we develop the notion of screen isoparametric hypersurface for null hypersurfaces of Robertson–Walker spacetimes. Using this formalism we derive... 
Mathematics, general | Mathematics | Secondary 53C50 | isoparametric hypersurfaces | Null hypersurfaces | Primary 53B30 | MATHEMATICS | MATHEMATICS, APPLIED | REAL HYPERSURFACES
Journal Article
Advances in Geometry, ISSN 1615-715X, 04/2019, Volume 19, Issue 2, pp. 235 - 250
We prove that every biharmonic hypersurface having constant higher order mean curvature for > 2 in a space form ) is of constant mean curvature. In particular,... 
mean curvature vector | 53C42 | 53C40 | 53D12 | isoparametric hypersurfaces | Biharmonic submanifolds | MATHEMATICS | CLASSIFICATION | SUBMANIFOLDS | Curvature | Hyperspaces
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 11/2014, Volume 25, Issue 12, pp. 1450117 - 1-1450117-9
In this paper, we prove that a Möbius isoparametric hypersurface is a Blaschke isoparametric hypersurface, and a Blaschke isoparametric hypersurface is a... 
Möbius invariants | Möbius isoparametric hypersurface | Blaschke isoparametric hypersurface | MATHEMATICS | Mobius invariants | DISTINCT PRINCIPAL CURVATURES | SUBMANIFOLDS | N+1 | CLASSIFICATION | MOBIUS | IMMERSED HYPERSURFACES | Mobius isoparametric hypersurface | UNIT-SPHERE | Eigenvalues | Mathematical analysis | Tensors
Journal Article
Annals of Global Analysis and Geometry, ISSN 0232-704X, 12/2017, Volume 52, Issue 4, pp. 425 - 456
Journal Article
数学学报:英文版, ISSN 1439-8516, 2016, Volume 32, Issue 6, pp. 715 - 724
Let x : M^n-1→ R^n be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of M under the Laguerre transformation group of... 
主曲率 | 常数 | 自由曲面 | 超曲面 | 标量曲率 | 不变量 | 变换群 | 各向同性 | Laguerre second fundamental form | Laguerre form | 53B25 | Mathematics, general | Mathematics | Laguerre metric | 53A40 | parallel Laguerre form | Laguerre isoparametric hypersurface
Journal Article
Advances in Geometry, ISSN 1615-715X, 04/2018, Volume 18, Issue 2, pp. 187 - 192
After nearly 50 years of research the Chern conjecture for isoparametric hypersurfaces in spheres is still an unsolved and important problem. Here we give a... 
constant Gauß–Kronecker curvature | 53C42 | 53C40 | CMC hypersurface | isoparametric hypersurface | Chern conjecture
Journal Article
Turkish Journal of Mathematics, ISSN 1300-0098, 2018, Volume 42, Issue 3, pp. 1180 - 1191
In this paper, we classify umbilic-free hypersurfaces of the unit sphere that have constant para-Blaschke eigenvalues and possess parallel Mobius form. To... 
Parallel Möbius form | Möbius second fundamental form | Möbius form | Möbius metric | Blaschke tensor | Mobius second fundamental form | DISTINCT PRINCIPAL CURVATURES | Mobius form | parallel Mobius form | ISOPARAMETRIC HYPERSURFACES | CLASSIFICATION | IMMERSED HYPERSURFACES | UNIT-SPHERE | MATHEMATICS | SUBMANIFOLDS | S-N | Mobius metric | GEOMETRY
Journal Article
数学年刊:B辑英文版, ISSN 0252-9599, 2017, Volume 38, Issue 5, pp. 1131 - 1144
Let x : M^n→S^n+1 be an immersed hypersurface in the (n +1)-dimensional sphere S^n+1. If, for any points p,q ∈ M^n, there exists a Mobius transformation Ф :... 
球面 | 主曲率 | 均匀 | Mobius变换 | 超曲面 | 莫比乌斯曲面 | 浸入曲面 | 53C40 | 53A30 | Mathematics, general | Mathematics | Conformal transformation group | Applications of Mathematics | Möbius isoparametric hypersurfaces | Möbius transformation group | Möbius homogeneous hypersurfaces
Journal Article
Advances in Mathematics, ISSN 0001-8708, 05/2014, Volume 256, pp. 156 - 205
A hypersurface without umbilics in the (n+1)-dimensional Euclidean space f:Mn→Rn+1 is known to be determined by the Möbius metric g and the Möbius second... 
Rigidity theorem | Cartan hypersurfaces | Bonnet surfaces | Reduction theorem | Möbius metric | Deformation of submanifolds | MATHEMATICS | SUBMANIFOLDS | ISOPARAMETRIC HYPERSURFACES | CURVATURE | Mobius metric
Journal Article
REVISTA DE LA UNION MATEMATICA ARGENTINA, ISSN 0041-6932, 2017, Volume 58, Issue 2, pp. 215 - 226
We show that metallic shaped hypersurfaces in Lorentzian space forms are isoparametric and obtain their full classification. 
MATHEMATICS | Lorentzian space form | MATHEMATICS, APPLIED | metallic shaped hypersurface | CLASSIFICATION | isoparametric hypersurface | RIEMANNIAN-MANIFOLDS
Journal Article
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