复流形上的CR-子流形

CR - Submanifolds of a Complex Manifold

利用不变形式的方法对复流形上的CR—子流形进行了一定的研究。首先考虑外围空间是复空间型的情形,得到了子流形是平坦流形或CR—乘积的条件,进一步考虑外围流形为更一般的不定复空间型,得到了它的子流形是全纯子流形和类空全纯子流形的条件。

In this paper we study CR - submanifolds of a complex manifold using the method of the invariant form. First, we obtain the condition that a submanifold is a flat manifold or CR - product on the condition that peripheral space is a complex space form. Furthermore, we get the condition that its submanifold is holomorphic submanifold and space - like submanifold under the condition that peripheral manifold is indefinite complex space form.