Decompositions and complexifications of homogeneous spaces

TL;DR

This paper extends a decomposition theorem for Finsler symmetric spaces with semi-negative curvature and applies it to describe the complexification of certain infinite-dimensional homogeneous spaces.

Contribution

It generalizes the CPR decomposition theorem to Finsler symmetric spaces and provides a geometric framework for their complexification.

Findings

Extended CPR decomposition theorem for Finsler symmetric spaces.

Geometric description of complexified infinite-dimensional homogeneous spaces.

Application to reductive structures in differential geometry.

Abstract

In this paper an extended CPR decomposition theorem for Finsler symmetric spaces of semi-negative curvature in the context of reductive structures is proven. This decomposition theorem is applied to give a geometric description of the complexification of some infinite dimensional homogeneous spaces.