On CMC hypersurfaces in 𝕊n+1 with constant Gauß–Kronecker curvature

Abstract 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 partial result for CMC hypersurfaces with constant Gauß–Kronecker curvature, mainly using a result given in [3] by Otsuki.

A new structural approach to isoparametric hypersurfaces in spheres

Annals of Global Analysis and Geometry ◽

10.1007/s10455-017-9563-3 ◽

2017 ◽

Vol 52 (4) ◽

pp. 425-456 ◽

Cited By ~ 2

Author(s):

Anna Siffert

Keyword(s):

Structural Approach ◽

Isoparametric hypersurfaces in spheres, integrable nondiagonalizable systems of hydrodynamic type, and N-wave systems

Differential Geometry and its Applications ◽

10.1016/0926-2245(95)00022-4 ◽

1995 ◽

Vol 5 (4) ◽

pp. 335-369 ◽

Cited By ~ 19

Author(s):

E.V. Ferapontov

Keyword(s):

Hydrodynamic Type ◽

N Wave ◽

Hypersurfaces In Spheres ◽

Systems Of Hydrodynamic Type

An algebraic approach to isoparametric hypersurfaces in spheres, II

10.2748/tmj/1178229051 ◽

1983 ◽

Vol 35 (2) ◽

pp. 225-247 ◽

Cited By ~ 6

Author(s):

Josef Dorfmeister ◽

Erhard Neher

Keyword(s):

Algebraic Approach ◽

On some types of isoparametric hypersurfaces in spheres, II

10.2748/tmj/1178240877 ◽

1976 ◽

Vol 28 (1) ◽

pp. 7-55 ◽

Cited By ~ 33

Author(s):

Hideki Ozeki ◽

Masaru Takeuchi

Keyword(s):

An algebraic approach to isoparametric hypersurfaces in spheres, I

10.2748/tmj/1178229050 ◽

1983 ◽

Vol 35 (2) ◽

pp. 187-224 ◽

Cited By ~ 5

Author(s):

Josef Dorfmeister ◽

Erhard Neher

Keyword(s):

Algebraic Approach ◽

MOMENT MAPS AND ISOPARAMETRIC HYPERSURFACES IN SPHERES — HERMITIAN CASES

Transformation Groups ◽

10.1007/s00031-015-9305-1 ◽

2015 ◽

Vol 20 (2) ◽

pp. 417-436

Author(s):

SHINOBU FUJII ◽

HIROSHI TAMARU

Keyword(s):

Moment Maps ◽

On Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres

Mathematische Zeitschrift ◽

10.1007/s00209-008-0350-5 ◽

2008 ◽

Vol 261 (4) ◽

pp. 749-785 ◽

Cited By ~ 13

Author(s):

Hui Ma ◽

Yoshihiro Ohnita

Keyword(s):

Lagrangian Submanifolds ◽

Classification of isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$

Proceedings of the American Mathematical Society ◽

10.1090/proc/12924 ◽

2015 ◽

Vol 144 (5) ◽

pp. 2217-2230 ◽

Cited By ~ 3

Author(s):

Anna Siffert

Keyword(s):

On some types of isoparametric hypersurfaces in spheres, I

10.2748/tmj/1178240941 ◽

1975 ◽

Vol 27 (4) ◽

pp. 515-559 ◽

Cited By ~ 46

Author(s):

Hideki Ozeki ◽

Masaru Takeuchi

Keyword(s):

Lagrangian geometry of the Gauss images of isoparametric hypersurfaces in spheres

Complex Manifolds ◽

10.1515/coma-2019-0013 ◽

2019 ◽

Vol 6 (1) ◽

pp. 265-278

Author(s):

Reiko Miyaoka ◽

Yoshihiro Ohnita

Keyword(s):

Lagrangian Submanifolds ◽

Joint Work ◽

Standard Sphere ◽

Survey Article ◽

Complex Hyperquadric ◽

Hypersurfaces In Spheres ◽

Lagrangian Geometry

AbstractThe Gauss images of isoparametric hypersufaces of the standard sphere Sn+1 provide a rich class of compact minimal Lagrangian submanifolds embedded in the complex hyperquadric Qn(ℂ). This is a survey article based on our joint work [17] to study the Hamiltonian non-displaceability and related properties of such Lagrangian submanifolds.