Isometric immersions into Lorentzian products

Julien Roth (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We give a necessary and sufficient condition for an $n$-dimensional Riemannian manifold to be isometrically immersed into one of the Lorentzian products $\Ss^n\times\R_1$ or $\HH^n\times\R_1$. This condition is expressed in terms of its first and second fundamental forms, the tangent and normal projections of the vectical vector field. As applications, we give an equivalent condition in a spinorial way and we deduce the existence of a one-parameter family of isometric maximal deformation of a given maximal surface obtained by rotating the shape operator.

Mots clés: Isometric Immersions; Gauss and Codazzi Equations; Maximal surfaces; Spinors

Domaines: Géométrie différentielle [math.DG]

Julien Roth. Isometric immersions into Lorentzian products. International Journal of Geometric Methods in Modern Physics, 2011, 8 (6), pp 1-22. ⟨hal-00528583⟩