Curvature explosion in quotients and applications

TL;DR

This paper proves that quotient spaces of variationally complete group actions form good Riemannian orbifolds and extends the result to singular Riemannian foliations without horizontal conjugate points.

Contribution

It establishes a new connection between variationally complete group actions and the structure of Riemannian orbifolds, generalizing to singular foliations.

Findings

Quotient space of variationally complete group action is a good Riemannian orbifold

Extension of results to singular Riemannian foliations without horizontal conjugate points

Provides new insights into the geometry of quotient spaces and foliations

Abstract

We prove that the quotient space of a variationally complete group action is a good Riemannian orbifold. The result is generalized to singular Riemannian foliations without horizontal conjugate points.