Invariant proper metrics on coset spaces
  It is known that for every second countable locally compact group G, there exists a proper G-invariant metric which induces the topology of the group. This is no longer true for coset spaces G/H viewed as G-spaces. We study necessary and sufficient conditions which ensure the existence of such metrics on G/H. 
Claire Anantharaman-Delaroche (MAPMO)
math.GN