Vector Fields and Differential Forms on the Orbit Space of a Proper Action

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.

Keywords

• proper action
• orbit space
• vector field on orbit space
• differential forms on orbit space