Let M be a Riemannian manifold with a polar action by the Lie group G,
with section Σ⊂M and generalized Weyl group W. We show that
restriction to Σ is a surjective map from the set of smooth
G-invariant tensors on M onto the set of smooth W-invariant tensors on
Σ. Moreover, we show that every smooth W-invariant Riemannian metric
on Σ can be extended to a smooth G-invariant Riemannian metric on M
with respect to which the G-action remains polar with the same section
Σ.Comment: arXiv admin note: text overlap with arXiv:1205.476