Cartan Spaces and Natural Foliations on the Cotangent Bundle

TL;DR

This paper explores the geometry of natural foliations in the cotangent bundle of Cartan spaces, revealing their close relationship to the underlying space and providing new characterizations of spaces with negative constant curvature.

Contribution

It introduces a novel approach linking foliation geometry in cotangent bundles to properties of Cartan spaces, especially those with negative constant curvature.

Findings

Foliation geometry closely relates to the Cartan space's geometry.

New characterizations of Cartan spaces with negative constant curvature.

Enhanced understanding of the structure of cotangent bundles in Cartan geometry.

Abstract

In this paper, the natural foliations in cotangent bundle T*M of Cartan space (M,K) are studied. It is shown that the geometry of these foliations is closely related to the geometry of the Cartan space (M,K) itself. This approach is used to obtain new characterizations of Cartan spaces with negative constant curvature.