The book [*Directional Statistics*][1] by Mardia and Jupp discusses concrete examples of distributions on:

1. Surface of the unit hypersphere
2. On Stiefel Manifolds
3. Maybe some others

**EDIT** In particular, have a look at §13.4.2 that discusses distributions on more general manifolds (e.g., on compact Riemannian manifolds). That section also provides several useful references.

I also recalled another source that might be useful to you:

[*Matrix Variate Distributions*][2] by Gupta and Nagar. In particular, see chapter 8.



  [1]: http://books.google.com/books?id=PTNiCm4Q-M0C&dq=directional+statistics&source=gbs_navlinks_s
  [2]: http://www.amazon.com/Variate-Distributions-Monographs-Surveys-Mathematics/dp/1584880465