In this case the tangent spaces to N will be identified with subspaces to tangent spaces to
M in the natural way.
It is my pleasure to acknowledge, first of all, Ted Shifrin who spent a morning explaining
the results of  to me. This got me hooked on the idea of trying to understand kinematic
formulas in the context of Riemannian homogeneous spaces. This paper is very much a
result of that conversation. I also would like to thank Paul Hewitt for some conversations on
invariant theory which greatly speeded up my coming up with the correct formulation and
proof of theorem 9.9. Finally the referee made a very thorough reading of the manuscript
and made suggestions leading to numerous improvements.