Suppose that $G$ is a Lie group (not necessarily compact) and $P$ and $H$ are two closed Lie subgroups. Does anyone happen to know of some good references that cover the double coset space/biquotient $P\backslash G/H$? I haven't had much luck finding information about this (and only a little bit in the case $G$ is compact).
For example, $G/H$ is obviously a smooth homogeneous space, but is $P \backslash G/H$ even a manifold in general?