Vector fields and differential forms on the orbit space of a proper action

TL;DR

This paper develops an intrinsic framework for understanding vector fields and differential forms on the orbit space resulting from a proper Lie group action, enhancing geometric analysis in this context.

Contribution

It introduces a new intrinsic approach to define vector fields and differential forms on orbit spaces of proper Lie group actions, based on generators of infinitesimal diffeomorphisms.

Findings

Provides a consistent definition of differential forms on orbit spaces.

Establishes a framework for vector fields on orbit spaces.

Enhances understanding of geometric structures in quotient spaces.

Abstract

In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This yields an intrinsic view of vector fields and differential forms on the orbit space.