On curves and jets of curves and on supermanifolds

TL;DR

This paper explores the concept of curves and jets on supermanifolds, defines higher order tangent bundles geometrically, and compares these notions with existing literature to clarify their relationships.

Contribution

It introduces a natural definition of curves and jets on supermanifolds and provides a geometric construction of higher order tangent bundles.

Findings

Defined a natural concept of curves on supermanifolds

Constructed higher order tangent bundles geometrically

Compared new notions with existing literature

Abstract

In this note we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we make a quick comparison with the notion of a curve presented here are other common notions found in the literature.