一类不定复空间型中Lagrange子流形的Chen型不等式

摘要

利用 Riemann 不变量和 Riemann 流形上的最优化方法得到一类不定复空间型中Lagrange子流形的Chen型不等式，并证明了等号成立时子流形一定为全测地的。%We obtained an inequality of Chen type for Lagrangian submanifolds of a class of indefinite complex space form using the Riemannian invariant and the optimization method on the Riemannian manifolds.In particular,we also showed that a Lagrangian submanifold of the indefinite complex space form attaining equality in the inequality must be totally geodesic.