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A classification of pseudo-parallel hypersurfaces of S-n x R and H-n x R

Author:
Lobos, G. A.  Tassi, M. P.  


Journal:
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS


Issue Date:
2019


Abstract(summary):

In this work we complete a classification of pseudo-parallel hypersurfaces of S-n x R and H-n x R, that was partially given by F. Lin and B. Yang. As an application, we obtain a classification of pseudo-parallel hypersurfaces with constant mean curvature. In particular, we prove that a minimal pseudo-parallel hypersurface is either a totally geodesic hypersurface, a minimal rotation hypersurface or a cylinder over a generalized Clifford torus in S-n. Moreover, we prove that any pseudo-parallel hypersurface is a pseudo-symmetric manifold in the sense of R. Deszcz. (C) 2018 Elsevier B.V. All rights reserved.


Page:
72---82


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