The first eigenvalue of the Laplacian on a certain generalized flag manifold (Q1100743)

Let \((M,g)\) be a compact Riemannian manifold and let \(\lambda_ 1(g)\) be the first positive eigenvalue of the Laplacian \(\Delta =d^*d\) acting on functions. Let M be a generalized flag manifold - i.e. \(M=G/K\) where G is a compact connected Lie group and K is the centralizer of a toral subgroup. The authors show if X has the reducible isotropy action, then there exists a family of invariant metrics \(g_ t\) so that (a) vol\((M,g_ t)=1\) and (b) \(\lim_{t\to \infty}\lambda_ 1(g_ t)=\infty\).