کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4605846 1631353 2015 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms
ترجمه فارسی عنوان
هیپرپروفی های هاف در فرم های فضایی پیچیده و پارازیتی شبه ریمان
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 42, October 2015, Pages 1–14
نویسندگان
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