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

2015 ◽  
Vol 144 (5) ◽  
pp. 2217-2230 ◽  
Author(s):  
Anna Siffert
Keyword(s):  
Isoparametric Hypersurfaces ◽  
Hypersurfaces In Spheres

Classification of Möbius Isoparametric Hypersurfaces in ${\Bbb S}^5$

2006 ◽  
Vol 151 (3) ◽  
pp. 201-222 ◽  
Author(s):  
Zejun Hu ◽  
Haizhong Li ◽  
Changping Wang
Keyword(s):  
Isoparametric Hypersurfaces

scholarly journals A Class of Special Hypersurfaces in Real Space Forms

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yan Zhao ◽  
Ximin Liu
Keyword(s):  
Real Space ◽  
Principal Curvatures ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Real Space Forms ◽  
Constant Principal Curvatures

We define the generalized golden- and product-shaped hypersurfaces in real space forms. A hypersurfaceMin real space formsRn+1,Sn+1, andHn+1is isoparametric if it has constant principal curvatures. Based on the classification of isoparametric hypersurfaces, we obtain the whole families of the generalized golden- and product-shaped hypersurfaces in real space forms.

Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Fengyun Zhang ◽  
Huafei Sun
Keyword(s):  
Conformal Transformation ◽  
Transformation Group ◽  
Second Fundamental Form ◽  
Conformal Metric ◽  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Lorentzian Space ◽  
Blaschke Tensor ◽  
Lorentzian Space Forms

AbstractIn this paper, we study regular immersed hypersurfaces in Lorentzian space forms with a conformal metric, a conformal second fundamental form, the conformal Blaschke tensor and a conformal form, which are invariants under the conformal transformation group. We classify all the immersed hypersurfaces in Lorentzian space forms with two distinct constant Blaschke eigenvalues and vanishing conformal form.

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