Induced geometry from disformal transformation

TL;DR

This paper explores how disformal transformations can induce a new geometric structure from Riemannian manifolds, generalizing Weyl integrable and Weyl geometries.

Contribution

It introduces a novel geometric framework derived from disformal transformations, extending the concept of Weyl geometries.

Findings

Disformal transformations induce a new geometric structure from Riemannian manifolds.

The resulting geometry generalizes Weyl integrable geometry.

A further generalized geometry related to Weyl geometry is proposed.

Abstract

In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these results, we further propose a geometry which is naturally a generalization of Weyl geometry.