Invariant Hermitian structures and variational aspects of a family of holomorphic curves on flag manifolds

Abstract

In this article, we study variational aspects for a special class of holomorphic maps on flag manifolds. We prove stability and non-stability results for such maps with respect to a large number of invariant Hermitian structures on maximal flag manifolds including the (1, 2)-symplectic structures, Einstein metrics, Cartan–Killing metrics, and so on. Some results in this article were announced without proofs in a past article by the first author.