3 problems

Let $G$ be a semi-simple Lie group acting effectively and isometrically on a connected Riemannian manifold $M$, and let $X\in\mathfrak{g}=\operatorname{Lie}(G)$. Suppose that $X$ d…

Let $(M,g)$ be a Riemannian manifold with Lie algebra $\mathfrak{g}$ of Killing fields, and let $X e 0$ be a Killing field of constant length. A vector $X$ is compact in…

Deformation-law conjecture. If $\mathcal{G}\subset\mathcal{P}$, then there exist deformation laws of this form such that $\eta_{ab}$ is flat and every $X\in\mathcal{G}$ is a Killin…