Abstract:

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.

Key words: indefinite complex space form, Lagrangian submanifolds, inequality of Chen type, totally geodesic