The index and certain stability of minimal anti invariant submanifolds in Sasakian and Kähler Manifolds

Abstract

The index forms of minimal anti invariant submanifolds in Sasakian and Kähler manifolds are obtained. We give lower bounds for the index of these submanifolds in terms of their intrinsic quantities. Certain stability of the minimal submanifolds is also considered, which is related to eigenspaces of the Laplacian.