arXiv subjects

Ricardo A. E. Mendes

Publications and source records attributed to Ricardo A. E. Mendes.

20 records · Page 2Linked to original sources

arXiv2013

Extending tensors on polar manifolds

Let $M$ be a Riemannian manifold with a polar action by the Lie group $G$, with section $Σ\subset M$ 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 $Σ$.

math.DG↗

arXiv2012

Lifting tensors from orbifold quotients

We deal with a Lie group G acting by isometries on a Riemannian manifold M, such that the quotient M/G is an orbifold, or, equivalently, all slice representations are polar. We show that any smooth orbifold symmetric 2-tensor on M/G lifts to a smooth G-invariant symmetric 2-tensor on M. The proof relies on a fact about the Invariant Theory of finite reflection groups which may be of independent interest.

math.DG↗