Riemannian ${\lambda }_1$-extremal Metrics on Generalized Flag Manifolds

Abstract

In this work, we will expose new classification results concerning ${\lambda }_1$-extremality for partial flag manifolds using a sufficient and necessary condition, in terms of Lie theoretic data, for a Kähler-Einstein metric over a generalized flag manifold to be a critical point for the functional that assigns for each Riemannian metric its first positive eigenvalue of the associated Laplacian.