scholarly journals A new structural approach to isoparametric hypersurfaces in spheres

2017 ◽  
Vol 52 (4) ◽  
pp. 425-456 ◽  
Author(s):  
Anna Siffert
Keyword(s):  
Structural Approach ◽  
Isoparametric Hypersurfaces ◽  
Hypersurfaces In Spheres

scholarly journals On some types of isoparametric hypersurfaces in spheres, I

1975 ◽  
Vol 27 (4) ◽  
pp. 515-559 ◽  
Author(s):  
Hideki Ozeki ◽  
Masaru Takeuchi
Keyword(s):  
Isoparametric Hypersurfaces ◽  
Hypersurfaces In Spheres

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

2018 ◽  
Vol 18 (2) ◽  
pp. 187-192
Author(s):  
S. C. de Almeida ◽  
F. G. B. Brito ◽  
M. Scherfner ◽  
S. Weiss
Keyword(s):  
Partial Result ◽  
Isoparametric Hypersurfaces ◽  
Hypersurfaces In Spheres

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.

scholarly journals Lagrangian geometry of the Gauss images of isoparametric hypersurfaces in spheres

2019 ◽  
Vol 6 (1) ◽  
pp. 265-278
Author(s):  
Reiko Miyaoka ◽  
Yoshihiro Ohnita
Keyword(s):  
Lagrangian Submanifolds ◽  
Joint Work ◽  
Standard Sphere ◽  
Isoparametric Hypersurfaces ◽  
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.

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