Foliations of doubly warped products by k-umbilical hypersurfaces


Por: Gervasio Colares, A., Palmas, Oscar

Publicada: 1 oct 2022
Categoría: Applied mathematics

Resumen:
A k-umbilical hypersurface of a (n + 1)-dimensional semi-Riemannian manifold has k equal principal curvatures at each point. We study conditions under which a Lorentzian manifold admits a foliation by such hypersurfaces. Originally motivated by the existence of particular foliations of the Schwarzschild black hole, we extend our theory to the class of manifolds given as doubly warped products. The key ingredient for our study is a new class of vector fields which includes conformal vector fields. After obtaining general results about manifolds admitting such kind of vector fields, we give a characterization of the Schwarzschild black hole in the class of Lorentzian manifolds admitting a pair of such vector fields and satisfying some boundary conditions.

Filiaciones:
Gervasio Colares, A.:
 Univ Fed Ceara, Dept Matemat, Av Humberto Monte S-N,Campus Pici,Bloco 914, BR-60455760 Fortaleza, Ceara, Brazil

Palmas, Oscar:
 Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Ciudad Univ, Mexico City 04510, DF, Mexico
ISSN: 03733114





ANNALI DI MATEMATICA PURA ED APPLICATA
Editorial
Springer-Verlag, TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY, Alemania
Tipo de documento: Article
Volumen: 201 Número: 5
Páginas: 2261-2285
WOS Id: 000762888000001