Minimal immersion of pseudo-Riemannian manifolds
Let \(f\) be an isometric immersion of a pseudo-Riemannian manifold in a pseudo-Euclidean space, such that \(\Delta f=bf\), for some constant \(b\neq 0\). The author proves that \(f\) realizes a minimal immersion in a pseudo- Riemannian sphere or in a pseudo-hyperbolic space, provided \(b>0\) or \(b<0\) respectively. Then he obtains the spectrum for both, the pseudo- Riemannian sphere and the pseudo-hyperbolic space.
scientific article; zbMATH DE number 109325