A quadric representation of pseudo-Riemannian product immersions

概要

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In this paper we introduce a quadric representation φ of the product of two pseudo-Riemannian isometric immersions. We characterize the product of submanifolds whose quadric representation satisfies △Hφ=λHφ、for a real constant λ, where Hφ is the mean curvature vector field of .φ As for hypersurfaces, we prove that the only ones satisfying that equation are minimal products as well as products of a minimal hypersurface and another one which has constant mean and constant scalar curvatures with an appropriate relation between them. In particular, the family of these surfaces consists of H2(-1) and S1(2/3)×1(-2) in S13(1) and S12(1), H11(-2/3)×1(2). S11(2)×1(-2/3) and a B-scroll over a null Frenet curve with torsion ±√2 in H13(-1).
筑波大学の論文
1997-01-10