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

Autor(es)

Anciaux, Henri ^[1] ; Panagiotidou, Konstantina ^[2]

Afiliação do(s) autor(es)

^[1] Univ Libre Bruxelles, Geometrie Differentielle, B-2131050 Brussels - Belgium

^[2] Hellen Mil Acad, Fac Math & Engn Sci, Attiki - Greece

• Tipo de documento: Artigo Científico
• Fonte: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS; v. 42, p. 1-14, OCT 2015.
• Citações Web of Science: 2

Resumo

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)

• Processo FAPESP: 11/21362-2 - Ações de grupos, teoria de subvariedades, e análise global em geometria Riemanniana e pseudo-riemanniana
• Beneficiário: Paolo Piccione
• Modalidade de apoio: Auxílio à Pesquisa - Temático