2 problems

Let $G$ be a compact Lie group with a bi-invariant metric $h_0$ and Lie algebra $\mathfrak g$. For a left-invariant metric $h$ on $G$, let $\Phi$ be the unique $h_0$-self-adjoint p…

Let $G$ be a compact connected Lie group, and let $\mathcal M^G$ denote the space of left-invariant Riemannian metrics on $G$. For $g\in\mathcal M^G$, write $\lambda_1(G,g)$ for th…