Killing sections and sigma models with Lie algebroid targets

Abstract

We define and examine the notion of a Killing section of a Riemannian Lie algebroid as a natural generalisation of a Killing vector field. We show that the various expression for a vector field to be Killing naturally generalise to the setting of Lie algebroids. As an application we examine the internal symmetries of a class of sigma models for which the target space is a Riemannian Lie algebroid. Critical points of these sigma models are interpreted as generalised harmonic maps.

11 pages. Comments welcomed

References in corpus (6)

• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Killing and Conformal Killing tensors
• Jacobi vector fields for Lagrangian systems on algebroids
• Gravity theory on Poisson manifold with $R$-flux
• Einstein-Cartan Algebroids and Black Holes in Solitonic Backgrounds
• Metrizable linear connections in a Lie algebroid

Cited by in corpus (3)

• Gravity theory on Poisson manifold with $R$-flux
• Contact structures on Lie algebroids
• Carrollian Lie Algebroids: Taming Singular Carrollian Geometries