Volumes of compact manifolds (Q1430986)

The authors compute the volume of a series of compact Riemannian manifolds which play a role or appear in problems in physics. They treat a series of homogeneous spaces, more precisely spheres, projective spaces, some group manifolds and generalized flag manifolds. In all these cases they propose a natural normalization, i.e., a generalization of the unit radius condition for spheres. Most of these results are known and are already available in the literature but they are presented here in such a way that they are, at least in the opinion of the authors, useful for and easier to apply by physicists.