All Questions

Is there a Riemannian metric on $\mathbb{R}^2$ (or a $2$ dimensional manifold) such that the intersection of every two open discs is an open disc, again? As linear version of this question we ask: ...

Let $G$ be a compact Lie group with a biinvariant metric. Note that $G\times G$ acts isometrically on $G$ from left and right. Consider the quotient $D=G/H$ by a closed subgroup $H\le G\times G$; if $...