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
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