Isometric immersions of pseudo-Riemannian space forms |
| |
Affiliation: | 1. Department of Emergency Medicine, Hospital of South West Jutland, Esbjerg, Denmark;2. Faculty Internal Medicine, Mercy Medical Center, Redding, CA, USA |
| |
Abstract: | In this paper we study local isometric immersions f:Msn(K)→Ns+q2n−1(c) of a time-like n-submanifold Msn(K) with constant sectional curvature K and index s into a pseudo-Riemannian space form Ns+q2n−1(c) with constant sectional curvature c and index s+q, where q≥0, 1≤s≤n−1 and K≠c. We first prove the existence of Chebyshev coordinates of a time-like submanifold Msn(K) in certain conditions. Afterwards, we generalize the classical Bäcklund theorem for space-like (or time-like) submanifolds in Nn−12n−1(c) and N12n−1(c). Finally as an application, in the Chebyshev coordinates, we use the Bäcklund theorem to give a Bäcklund transformation and a permutability formula between the generalized sine-Laplace equation and the generalized sinh-Laplace equation. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|