A note on Clifford bundles and certain Finsler type spaces

TL;DR

This paper explores the connection between Clifford bundles and Finsler structures, extending classical relations to more general geometric settings and establishing a triangle map for flat metrics.

Contribution

It introduces a novel relation between Clifford bundle extensions and Finsler structures, generalizing the Clifford relation to broader geometric contexts.

Findings

Established a triangle map for flat metrics relating Finsler structures and Clifford bundles

Extended the classical Clifford relation to Finsler type spaces

Provided insights into Dirac operators in generalized geometric frameworks

Abstract

We study a relation between certain extensions of the Clifford bundle and Finsler type structures that naturally generalize the standard Clifford relation between (pseudo)-Riemannian metric structures and Dirac matrices. We show for flat metrics that there is a triangle map between Finsler structures constructed from an (pseudo)-Riemannian metric and $1$-forms on $M$, the extension of the Clifford bundle and relevant Dirac type operators.