Dense


Abstract for

"A note on the denseness of complete invariant metrics"

(joint work with C. Varga)

In this paper we prove that, given a compact Lie group action on a manifold, the space of complete G-invariant riemannian metrics on M is dense in the space of all G-invariant riemannian metrics. Similar results are proved for Finsler metrics. This not only extends the known results for the non-equivariant case (the existence result of K. Nomizu-H. Oseki, and the denseness result of A. Morrow), but also simplifies the proofs considerably.