A note about invariant SKT structures and generalized Kahler structures on flag manifolds

TL;DR

This paper proves that all invariant SKT structures on flag manifolds of semisimple compact Lie groups are actually Kahler, and it describes invariant generalized Kahler structures on these manifolds.

Contribution

It establishes that invariant SKT structures on flag manifolds are necessarily Kahler and characterizes invariant generalized Kahler structures.

Findings

Invariant SKT structures are Kahler on flag manifolds.

Classification of invariant generalized Kahler structures on flag manifolds.

Simplification of the structure theory for invariant SKT and generalized Kahler geometries.

Abstract

We prove that any invariant strong Kahler structure with torsion (SKT structure) on a flag manifold M=G/K of a semisimple compact Lie group G is Kahler. As an application we describe invariant generalized Kahler structures on M.