scholarly journals Isoparametric hypersurfaces with four principal curvatures, IV

2020 ◽  
Vol 115 (2) ◽  
pp. 225-301
Author(s):  
Quo-Shin Chi
Keyword(s):  
Principal Curvatures ◽  
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.

Divergence-preserving geodesic transformations

1998 ◽  
Vol 128 (6) ◽  
pp. 1309-1323
Author(s):  
E. García-Río ◽  
L. Vanhecke
Keyword(s):  
Principal Curvatures ◽  
Isoparametric Hypersurfaces ◽  
Hopf Hypersurfaces ◽  
Geodesic Spheres ◽  
Constant Principal Curvatures ◽  
Volume Preserving ◽  
Special Classes

We discuss divergence- and volume-preserving geodesic transformations with respect to submanifolds and in particular, with respect to hypersurfaces. We use these transformations to derive characterisations of special classes of hypersurfaces such as isoparametric hypersurfaces and Hopf hypersurfaces with constant principal curvatures. Furthermore, we consider divergence-preserving geodesic transformations with respect to geodesic spheres.

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