2 problems

Let $N$ be a Riemannian manifold with sectional curvature at most $\delta<0$, and let $\gamma$ be a null-homotopic regular closed curve in $N$ whose length is greater than…

A locally compact group is compact-by-Lie if it has a compact normal subgroup such that the quotient is a Lie group. Let $G$ be a compactly generated locally compact group, and let…