Cheeger Deformations for Lie groupoid actions

TL;DR

This paper extends Cheeger's deformation techniques from Lie group actions to Lie groupoid actions on manifolds, providing explicit curvature descriptions for the generalized deformation.

Contribution

It introduces a novel extension of Cheeger's deformation to singular Riemannian foliations induced by Lie groupoid actions, with explicit curvature formulas.

Findings

Extended Cheeger deformation to Lie groupoid actions

Explicit sectional curvature formulas for the deformation

Applicable to singular Riemannian foliations

Abstract

We give an extension of Cheeger's deformation techniques for smooth Lie group actions on manifolds to the setting of singular Riemannian foliations induced by Lie groupoids actions. We give an explicit description of the sectional curvature of our generalized Cheeger deformation.