Finsler Metrics with Bounded Cartan Torsions

TL;DR

This paper identifies subclasses of Finsler metrics with bounded Cartan torsion, which is crucial for isometric immersion into Minkowski spaces, and shows these bounds can be independent of certain parameters.

Contribution

The paper introduces new subclasses of (?, ?)-metrics with bounded Cartan torsion, advancing understanding of their geometric properties and immersion capabilities.

Findings

Two subclasses of (?, ?)-metrics with bounded Cartan torsion identified.

Bounds on Cartan torsion can be independent of the norm of ?.

Provides conditions under which Cartan torsion remains bounded.

Abstract

The norm of Cartan torsion plays an important role for studying of immersion theory in Finsler geometry. Indeed, Finsler manifold with unbounded Cartan torsion can not be isometrically imbedded into any Minkowski space. In this paper, we find two subclasses of (?, ?)-metrics which have bounded Cartan torsion. Then, we give two subclasses of (?, ?)-metrics whose bound on the Cartan torsions are independent of the norm of ?.