scholarly journals Isoparametric hypersurfaces with four principal curvatures, III

2013 ◽  
Vol 94 (3) ◽  
pp. 469-504 ◽  
Author(s):  
Quo-Shin Chi
2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yan Zhao ◽  
Ximin Liu

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.


1998 ◽  
Vol 128 (6) ◽  
pp. 1309-1323
Author(s):  
E. García-Río ◽  
L. Vanhecke

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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