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 $TM\oplus {\Lambda }^p{T}^{\ast }M$ is an example leading to a scalar curvature of the form $R+H^2$ for a closed $(p+2)$-form $H$.

References in corpus (4)

• Generalised Geometry for M-Theory
• Generalized complex geometry
• NS-NS fluxes in Hitchin's generalized geometry
• On higher analogues of Courant algebroids

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• Metric-Connection Geometries on Pre-Leibniz Algebroids: A Search for Geometrical Structure in String Models
• Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
• Effective Actions for $\sigma$-Models of Poisson-Lie Type
• Omni $n$-Lie algebras and linearization of higher analogues of Courant algebroids
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• Exploration of The Duality Between Generalized Geometry and Extraordinary Magnetoresistance
• 'Anti-Commutable' Pre-Leibniz Algebroids and Admissible Connections
• Statistical Geometry and Hessian Structures on Pre-Leibniz Algebroids