Foliations of Tangent Bundle in a Finsler Manifold

TL;DR

This paper introduces a new frame on the tangent bundle of a Finsler manifold to facilitate the study of natural foliations and demonstrates that the indicatrix bundle with certain structures cannot be Sasakian.

Contribution

It proposes a novel frame on the tangent bundle of Finsler manifolds and analyzes the Sasakian properties of the indicatrix bundle with lifted structures.

Findings

The introduced frame simplifies the study of tangent bundle foliations.

The indicatrix bundle with lifted Sasaki metric and almost complex structure is not Sasakian.

Provides new insights into the geometric structures of Finsler manifolds.

Abstract

In this paper, a frame is introduced on tangent bundle of a Finsler manifold in a manner that it makes some simplicity to study the properties of the natural foliations in tangent bundle. Moreover, we show that the indicatrix bundle of a Finsler manifold with lifted sasaki metric and natural almost complex structure on tangent bundle cannot be a sasakian manifold.