广义复空间形式子流形平均曲率的一个讨论

Study of Mean Curvature of Submanifolds in Generalized Complex Space Forms

讨论了广义复空间形式的子流形的内蕴不变量与外蕴不变量之间的关系,利用高斯方程得到了子流形的平均区率这个外蕴不变量与一个内蕴不变量之间的不等式结论,给出了等式成立的充分必要条件.由于此不等式结果对于广义复空间形式的一般子流形均成立,并将此结果应用到广义复空间形式的斜子流形,得到一个推论.

The relationships between the intrinsic and the extrinsic invariants of submanifolds in generalized complex space forms are studied, and the inequalities of the mean curvature and an intrinsic invariant are obtained. The conditions of the inequalities are also presented. This resuit is hold for any submanifolds in generalized complex space forms, a corollary about slant submanifolds in generalized complex space forms is obtained by the inequalities.