The super-Sasaki metric on the antitangent bundle

Abstract

We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a generalisation of Sasaki's construction of a Riemannian metric on the tangent bundle of a Riemannian manifold.

7 pages. This new version has been extensively rewritten. Clarifying points, examples and minor typos have been corrected. Comments welcomed