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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

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Author(s):
Anciaux, Henri [1] ; Panagiotidou, Konstantina [2]
Total Authors: 2
Affiliation:
[1] Univ Libre Bruxelles, Geometrie Differentielle, B-2131050 Brussels - Belgium
[2] Hellen Mil Acad, Fac Math & Engn Sci, Attiki - Greece
Total Affiliations: 2
Document type: Journal article
Source: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS; v. 42, p. 1-14, OCT 2015.
Web of Science Citations: 2
Abstract

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel. (C) 2015 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 11/21362-2 - Group actions, submanifold theory and global analysis in Riemannian and pseudo-Riemannian geometry
Grantee:Paolo Piccione
Support Opportunities: Research Projects - Thematic Grants