On curves and jets of curves on supermanifolds

Andrew James Bruce

Address: Institute of Mathematics, Polish Academy of Sciences ul. Ĺšniadeckich 8, P.O. Box 21 00-956 Warszawa, Poland

E-mail: andrewjamesbruce@googlemail.com

Abstract: In this paper 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.

AMSclassification: primary 58A20; secondary 58A32, 58A50.

Keywords: supermanifolds, curves, jets, higher order tangent bundles.

DOI: 10.5817/AM2014-2-115