Abstract
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.
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Lira, J.H., Tojeiro, R. & Vitório, F. A Bonnet theorem for isometric immersions into products of space forms. Arch. Math. 95, 469–479 (2010). https://doi.org/10.1007/s00013-010-0183-4
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DOI: https://doi.org/10.1007/s00013-010-0183-4