# Mg.metric geometry – evenly uniform homogeneous spaces

Let's say we have a homogeneous space $$H setminus G$$.

Is it possible to say whether this homogeneous space admits a metric conforming to the structure only from its group structure?

I am particularly interested in a situation where $$H$$ is a noncompact subgroup at most $$G$$.

I hope my question does not seem too broad. Maybe this question has a trivial answer, but it's not obvious to a theoretical physicist.