Lifting tensors from orbifold quotients

2012/05/21 by Ricardo A. E. Mendes, Mendes, Ricardo A. E. · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1205.4765

24 pages

arxiv created 2012/05/21 · arxiv updated 2012/05/23

Abstract

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.

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• Extending tensors on polar manifolds

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