Geometric Structures and Differential Operators on Manifolds Having Super tangent Bundle

TL;DR

This paper introduces the concept of a super tangent bundle on manifolds and extends fundamental differential geometry notions like forms, connections, and metrics to this new setting.

Contribution

It presents the first systematic development of differential geometry tools on manifolds with super tangent bundles, expanding geometric analysis in supergeometry.

Findings

Defined super tangent bundle structures on manifolds.

Extended differential forms, exterior derivatives, and connections to supergeometry.

Laid groundwork for future studies in supergeometric differential operators.

Abstract

In this paper, we introduce the notion of a super tangent bundle of a manifold, and extend the basic notions of differential geometry such as differential forms, exterior derivation, connection, metric and divergence on manifolds that equipped with a super tangent bundle.