Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions

TL;DR

This paper introduces connections, torsion, and curvature for Leibniz algebroids, exemplifies a generalized Bismut connection, and derives a scalar curvature formula involving a closed form, expanding geometric frameworks.

Contribution

It develops a theory of connections and curvature for Leibniz algebroids and provides a specific example with a scalar curvature formula involving a closed form.

Findings

Defined connection, torsion, and curvature for Leibniz algebroids

Constructed a generalized Bismut connection on $TM igoplus igwedge^{p} T^{igast}M$

Derived a scalar curvature expression of the form $R + H^2$ for a closed $(p+2)$-form

Abstract

Connection, torsion and curvature are introduced for general (local) Leibniz algebroids. Generalized Bismut connection on $TM \oplus \Lambda^{p} T^{\ast}M$ is an example leading to a scalar curvature of the form $R + H^2$ for a closed $(p+2)$-form $H$.