Sobolev tests of goodness of fit of distributions on compact Riemannian   manifolds
  Classes of coordinate-invariant omnibus goodness-of-fit tests on compact Riemannian manifolds are proposed. The tests are based on Gin\'{e}'s Sobolev tests of uniformity. A condition for consistency is given. The tests are illustrated by an example on the rotation group $\mathit{SO}(3)$. 
P. E. Jupp