Publication details
Holonomy of supermanifolds
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Article in Periodical |
| Magazine / Source | Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.springerlink.com/content/l6grl32066017352/ |
| Field | General mathematics |
| Keywords | Supermanifold; Superconnection; Holonomy algebra; Berger superalgebra |
| Description | 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. |
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