Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions

Abstract

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

Keywords

• Generalized geometry
• Leibniz algebroid
• Bismut connection
• Torsion
• Curvature