凯勒流形[Kähler Manifold] - 达人(其实～我是卧底，来自外星)

2005/04/11 | 凯勒流形[Kähler Manifold]
类别(∑〖数学〗) | 评论(0) | 阅读(51) | 发表于 14:11: A complex manifold for which the exterior derivative of the fundamental form associated with the given Hermitian metric vanishes, so . In other words, it is a complex manifold with a Kähler structure. It has a Kähler form, so it is also a symplectic manifold. It has a Kähler metric, so it is also a Riemannian manifold.

The simplest example of a Kähler manifold is a Riemann surface, which is a complex manifold of dimension 1. In this case, the imaginary part of any Hermitian metric must be a closed form since all 2-forms are closed on a two real dimensional manifold.; 0