Sasaki空间形式中迷向极小积分子流形

Isotropic Minimal Integral Submanifolds of Sasakian Space Form

设M为Sasaki空间形式M-2n+1(c)中迷向极小积分子流形,对极小积分子流形已有众多研究.对迷向积分子流形,利用活动标架法并借助迷向子流形的等价条件,研究了该类子流形的刚性问题,获得了关于第二基本形式模长的Pinching定理:若M的第二基本形式模长平方‖σ‖2满足‖σ‖2≤81(n+2)(c+3),则M是全测地的.在一定意义下对文献(Yamaguchi S,Kon M,Ikawa T.J Differential Geom,1976,11:59-64.)的结果作了推广和改进.

Let M be an isotropic minimal integral submanfold of Sasakian space form. In this paper, a pinching theorem for the square of the length of the second fundamental form of M is obtained by using the method of moving frames and condition of equivalence of isotropic submanifolds, which generalizes and improves the result of literature（Yamaguchi S, Kon M, Ikawa T. J Differential Geom,1976,11：5964.