Holonomy of supermanifolds

Details Holonomy of supermanifolds Holonomy of supermanifolds

2007-03-22

arxiv.org/abs/math/0703679v3

Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg: 79 Issue1 (2009) 47--78

Mathematics

Differential Geometry

Extanded version, 33 pages

Scientific paper

10.1007/s12188-008-0015-7

Holonomy groups and holonomy algebras for connections on locally free sheaves over supermanifolds are introduced. A one-to-one correspondence between parallel sections and holonomy-invariant vectors, and a one-to-one correspondence between parallel locally direct subsheaves and holonomy-invariant vector supersubspaces are obtained. As the special case, the holonomy of linear connections on supermanifolds is studied. Examples of parallel geometric structures on supermanifolds and the corresponding holonomies are given. For Riemannian supermanifolds an analog of the Wu theorem is proved. Berger superalgebras are defined and their examples are given.

Affiliated with

Also associated with

No associations

Rating

Holonomy of supermanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Holonomy of supermanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holonomy of supermanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-168576