Isometric immersions into Lorentzian products (Q2891012)

The author investigates the necessary and sufficient conditions for isometric immersions of Riemannian/pseudo-Riemannian \(n\)-dimensional manifolds into Lorentzian products of \(S^n\times R_1\) or \(H^n\times R_1\). These conditions are expressed in terms of the first and second fundamental forms and the tangential and normal projections of a vertical vector field of the submanifold. After establishing these conditions, as an application the author gives an equivalent condition using spin geometry, and deduces the existence of a one-parameter family of isometric maximal deformations of a given maximal surface by rotation of the shape operator.NEWLINENEWLINE Contents include: Introduction; Preliminaries; The fundamental theorem of hypersurfaces; Application to maximal surfaces: The associate family; Spinorial characterization of surfaces into \(M^2(\kappa)\times R_1\); References (sixteen items).