伪黎曼流形的调和映射与极小浸入

Harmonic Maps and Minimal Immersions in Pseudo-Riemannian Manifold

本文讨论伪黎曼流形之间的调和映射与极小浸入。给出了能量泛函二阶变分的某些不稳定性以及调和映射与极小浸入之间的关系,对具有位似和调和Gauss映射的浸入,得到了一些与黎曼流形情形类似和完全不同的结论。

Discusses the harmonic maps and the minimal immersions between pseudo-Riemannian manifolds and non-definition of a second variation of harmonic maps. The relation of harmonic map with the minimal immersion between pseudo-Riemannian manifolds is given. Then considers the immersions with honothetic and harmonic Gauss map.