Spacelike surfaces which admit a nondegenerate null normal section in a Lorentzian space form
Metadatos
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Spacelike surface Gauss curvature Liebmann theorem
Fecha
2019Referencia bibliográfica
Publisher version: de la Fuente, D., Palomo, F.J. & Romero, A. On Non-degenerate Null Normal Sections of Codimension Two Spacelike Surfaces. Bull. Malays. Math. Sci. Soc. 42, 1451–1467 (2019). https://doi.org/10.1007/s40840-017-0557-x
Patrocinador
Spanish MINECO and ERDF project MTM2013-47828-C2-1-PResumen
In this paper, we develop a formula for spacelike surfaces in a 4-
dimensional Lorentzian space form which involves its mean curvature
vector eld and the Gauss curvature of the induced metric and the
Gauss curvature of the second fundamental form associated to a non-
degenerate null normal section. By means of this formula, we stablish
several su cient conditions for compact spacelike surfaces with con-
stant Gauss curvature to have a null umbilical direction. As another
application, we give a new proof of the Liebmann rigidity theorem in
Euclidean, hemispherical and hyperbolic spaces, and in the De Sitter
spacetime.