Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms
| Data(s) |
01/10/2015
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| 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. SCOPUS: ar.j SCOPUS: ar.j info:eu-repo/semantics/published |
| Formato |
1 full-text file(s): application/pdf |
| Identificador |
uri/info:doi/10.1016/j.difgeo.2015.05.004 uri/info:pii/S092622451500073X https://dipot.ulb.ac.be/dspace/bitstream/2013/204939/1/Elsevier_188566.pdf http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/204939 |
| Idioma(s) |
en |
| Direitos |
1 full-text file(s): info:eu-repo/semantics/restrictedAccess |
| Fonte |
Differential geometry and its applications, 42 |
| Palavras-Chave | #Géométrie #Analyse mathématique #Informatique mathématique #Hopf hypersurfaces #Pseudo-Riemannian geometry #Real hypersurfaces #Tubes |
| Tipo |
info:eu-repo/semantics/article info:ulb-repo/semantics/articlePeerReview info:ulb-repo/semantics/openurl/article |
