The super-Sasaki metric on the antitangent bundle
Differential Geometry
2020-07-17 v2 Mathematical Physics
math.MP
Symplectic Geometry
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.
Cite
@article{arxiv.2001.09724,
title = {The super-Sasaki metric on the antitangent bundle},
author = {Andrew James Bruce},
journal= {arXiv preprint arXiv:2001.09724},
year = {2020}
}
Comments
7 pages. This new version has been extensively rewritten. Clarifying points, examples and minor typos have been corrected. Comments welcomed