Abstract
Abstract
The notion of an odd quasi-connection on a supermanifold, which is loosely an affine connection that carries non-zero Grassmann parity, is examined. Their torsion and curvature are defined, however, in general, they are not tensors. A special class of such generalised connections, referred to as odd connections in this paper, have torsion and curvature tensors. Part of the structure is an odd involution of the tangent bundle of the supermanifold and this puts drastic restrictions on the supermanifolds that admit odd connections. In particular, they must have equal number of even and odd dimensions. Amongst other results, we show that an odd connection is defined, up to an odd tensor field of type (1, 2), by an affine connection and an odd endomorphism of the tangent bundle. Thus, the theory of odd connections and affine connections are not completely separate theories. As an example relevant to physics, it is shown that
N
=
1
super-Minkowski spacetime admits a natural odd connection.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Reference39 articles.
1. On q-deformed Levi-Civita connections;Arnlind
2. Riemannian geometry in spaces with Grassman coordinates;Arnowitt;Gen. Relativ. Gravit.,1976
3. Odd scalar curvature in anti-Poisson geometry;Batalin;Phys. Lett. B,2008
4. Supermanifolds;Berezin;Soviet Math. Dokl.,1975
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