2011/11/12 by Roland Knevel, Knevel, Roland
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:22F05 #msc:34A12 #msc:53C22 #msc:58A50
paper · pdf · doi:10.48550/arxiv.1111.2917
37 pages, no figures
arxiv created 2012/02/20 · arxiv updated 2012/02/21
Aim of this article is to introduce the notion of integral and geodesic flows on P-supermanifolds as certain partial actions of R . First I introduce the concept of parametrization over a `small' super algebra P, which leads to the notion of P-objects and is superized local deformation theory. It is shown how parametrization makes the theory much easier. A version of Palais' theorem for P-supermanifolds is obtained stating that every infinitesimal P-action of a simply connected P-super Lie group G on a P-supermanifold can be integrated to a whole action of G . Furthermore the faithful linearization of affine P-supermorphisms is proven. Finally I show that Newton's, Lagrange's and Hamilton's approach to mechanics can be formulated also for P- Riemannian supermanifolds and are infact equivalent.