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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
Advances in Mathematics, ISSN 0001-8708, 06/2013, Volume 239, pp. 1 - 17
Journal Article
Journal of Differential Geometry, ISSN 0022-040X, 2014, Volume 97, Issue 2, pp. 275 - 348
The image of the Gauss map of any oriented isoparametric hypersurface in the standard unit sphere Sn+1(1) is a minimal Lagrangian submanifold in the complex... 
HERMITIAN SYMMETRIC-SPACES | KAHLER-MANIFOLDS | MATHEMATICS | SPHERES | 4 PRINCIPAL CURVATURES | MINIMAL LAGRANGIAN SUBMANIFOLDS | SURFACES
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 10/2017, Volume 54, pp. 53 - 58
We generalise Ferus' work to study isoparametric hypersurfaces in semi-Riemannian space forms focusing, in this particular case, on anti-De Sitter spaces. We... 
Lorentzian space forms | Isoparametric hypersurface | Anti-De Sitter space | MATHEMATICS | MATHEMATICS, APPLIED | 4 PRINCIPAL CURVATURES
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 01/2020, Volume 2020, Issue 2, pp. 422 - 465
Abstract An isoparametric hypersurface in unit spheres has two focal submanifolds. Condition A plays a crucial role in the classification theory of... 
MATHEMATICS | DDVV CONJECTURE | TRIPLE-SYSTEMS | FOLIATION | SPHERE | EQUALITY | 4 PRINCIPAL CURVATURES | GEOMETRY
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2015, Volume 272, pp. 611 - 629
This paper extends widely the work in [11]. Existence and non-existence results of isoparametric functions on exotic spheres and Eells–Kuiper projective planes... 
Morse–Bott function | Eells–Kuiper projective plane | Isoparametric function | [formula omitted]-structure | Exotic sphere | 53C20 | Eells-Kuiper projective plane | Morse-Bott function | structure | 57R60 | MATHEMATICS | HYPERSURFACES | INVARIANT | 4 PRINCIPAL CURVATURES | MANIFOLDS | SCp-structure | CONJECTURE
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2016, Volume 368, Issue 2, pp. 1211 - 1249
Journal Article
Transformation Groups, ISSN 1083-4362, 6/2015, Volume 20, Issue 2, pp. 417 - 436
We study a relationship between isoparametric hypersurfaces in spheres with four distinct principal curvatures and the moment maps of certain Hamiltonian... 
Topological Groups, Lie Groups | Mathematics | Algebra | MATHEMATICS | SYMMETRIC-SPACES | 4 PRINCIPAL CURVATURES
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2017, Volume 286, Issue 3, pp. 1217 - 1226
Jakobson and Nadirashvili (J Differ Geom 53(1):177–182, 1999) constructed a sequence of eigenfunctions on $$T^2$$ T 2 with a bounded number of critical points,... 
53C40 | Eigenfunction of Laplacian | Critical set | 58J50 | Mathematics, general | Mathematics | Isoparametric hypersurface | 57R70 | MATHEMATICS | HYPERSURFACES | SPHERES | 1ST EIGENVALUE | 4 PRINCIPAL CURVATURES | YAU CONJECTURE | RIEMANNIAN-MANIFOLDS
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 06/2016, Volume 112, Issue 6, pp. 979 - 1001
In this paper, two sequences of minimal isoparametric hypersurfaces are constructed via representations of Clifford algebras. Based on these, we give estimates... 
CLIFFORD ALGEBRAS | LAPLACIAN | MATHEMATICS | HYPERSURFACES | SPHERES | HARMONIC-MAPS | MINIMAL SUBMANIFOLDS | 1ST EIGENVALUE | 4 PRINCIPAL CURVATURES | YAU CONJECTURE | MANIFOLDS | Geometry | Construction | Maps | Conferences | Mathematical analysis | Eigenvalues | Manifolds (mathematics) | Formulas (mathematics) | Mathematics - Differential Geometry
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 02/2013, Volume 31, Issue 1, pp. 130 - 139
We extend theorems of É. Cartan, Nomizu, Münzner, Q.M. Wang, and Ge–Tang on isoparametric functions to transnormal functions on a general Riemannian manifold.... 
Transnormal system | Transnormal function | Isoparametric hypersurface | Singular foliation | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | FAMILIES | ISOPARAMETRIC HYPERSURFACES | METRICS | 4 PRINCIPAL CURVATURES
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 10/2012, Volume 23, Issue 10, pp. 1250103 - 1250135
Journal Article
Annals of Global Analysis and Geometry, ISSN 0232-704X, 1/2013, Volume 43, Issue 1, pp. 47 - 62
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, 11/2016, Volume 70, Issue 3-4, pp. 499 - 531
We provide a complete local characterization of Dupin hypersurfaces in R-5, with four distinct principal curvatures, parametrized by lines of curvature. Such... 
53C42 | 53A07 | Moebius curvature | SPACE | MATHEMATICS | DIMENSIONS | MATHEMATICS, APPLIED | irreducible hypersurface | Dupin hypersurface | 4 PRINCIPAL CURVATURES | Laplace invariants | Lie curvature
Journal Article
Journal Article
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, ISSN 0926-2245, 10/2018, Volume 60, pp. 1 - 8
We classify the isoparametric functions on R-n x M-m, n, m >= 2, with compact level sets, where M-m is a connected, closed Riemannian manifold of dimension m.... 
MATHEMATICS | MATHEMATICS, APPLIED | Constant principal curvatures | SPACES | HYPERSURFACES | 4 PRINCIPAL CURVATURES | Isoparametric functions | Minimal submanifolds | Focal varieties | RIEMANNIAN-MANIFOLDS
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2014, Volume 57, Issue 9, pp. 1975 - 1982
We prove that there are only finitely many diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric... 
超曲面 | 有限性 | 紧凑 | 多类型 | 对称空间 | 曲率 | 微分同胚 | 单连通 | 53C20 | 53C40 | equifocal hypersurface | Mathematics | Applications of Mathematics | isoparametric hypersurface | focal point | finiteness | MATHEMATICS | MATHEMATICS, APPLIED | ISOPARAMETRIC HYPERSURFACES | 4 PRINCIPAL CURVATURES | Mathematical analysis | China
Journal Article
Analysis and Mathematical Physics, ISSN 1664-2368, 9/2014, Volume 4, Issue 3, pp. 237 - 245
Journal Article
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