  A class of causal variational principles on a compact manifold is introduced
and analyzed both numerically and analytically. It is proved under general
assumptions that the support of a minimizing measure is either completely
timelike, or it is singular in the sense that its interior is empty. In the
examples of the circle, the sphere and certain flag manifolds, the general
results are supplemented by a more detailed and explicit analysis of the
minimizers. On the sphere, we get a connection to packing problems and the
Tammes distribution. Moreover, the minimal action is estimated from above and
below.
