Axiomatic Differential Geometry II-4

TL;DR

This paper extends the axiomatic framework of differential geometry by deriving Jacobi-like identities for tangent-vector-valued forms from a general Jacobi identity, building on prior work.

Contribution

It introduces new Jacobi-like identities for tangent-vector-valued forms within an axiomatic differential geometry setting, expanding theoretical understanding.

Findings

Derived Jacobi-like identities for tangent-vector-valued forms

Extended axiomatic differential geometry framework

Connected identities to general Jacobi identity

Abstract

In our previous paper (Axiomatic Differential Geometry II-3) we have discussed the general Jacobi identity, from which the Jacobi identity of vector fields follows readily. In this paper we derive Jacobi-like identities of tangent-vector-valued forms from the general Jacobi identity.