A note on Clifford bundles and certain Finsler type spaces

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.