A Bonnet theorem for isometric immersions into products of space forms

摘要

We prove a Bonnet theorem for isometric immersions of semi-Riemannian manifolds into products of semi-Riemannian space forms. Namely, we give necessary and sufficient conditions for the existence and uniqueness (up to an isometry of the ambient space) of an isometric immersion of a semi-Riemannian manifold into a product of semi-Riemannian space forms.