The geodesic flow on a Riemannian supermanifold

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Garnier, Stephane ; Wurzbacher, Tilmann

关键词: Supermanifolds;    Riemannian metrics;    Geodesics;    Geodesic flow;   

DOI  :  10.1016/j.geomphys.2012.02.002

来源: Elsevier

【 摘 要 】

We give a natural definition of geodesics on a Riemannian supermanifold (M, g) and extend the usual geodesic flow on PM associated to the underlying Riemannian manifold (M, (g) over tilde) to a geodesic superflow on T*M. Integral curves of this flow turn out to be in natural bijection with geodesics on M. We also construct the corresponding exponential map and generalize the well-known faithful linearization of isometries to Riemannian superinanifolds. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free