Extending tensors on polar manifolds

2013/08/11 by Mendes, Ricardo A. E. · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1308.2412

Abstract

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.

Cited by

• On the Rational Hyperbolicity problem
• The dual foliation of polar actions on nonnegatively curved manifolds

Related

• Polar manifolds and actions
• Sections of polar actions
• Lifting tensors from orbifold quotients
• Low Dimensional Polar Actions
• Polar actions with a fixed point