2 problems

Let $(G/H,g)$ be a geodesic orbit Riemannian space, let $\mathfrak{g}=\operatorname{Lie}(G)$, and let $X\in\mathfrak{g}$ be a Killing field of constant length. Define … where…

Dušek's $k=0$ conjecture. For all null homogeneous geodesics in $G/H$, one has $k=0$ in the geodesic lemma.