| Title:
|
Non-split almost complex and non-split Riemannian supermanifolds (English) |
| Author:
|
Kalus, Matthias |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
229-238 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. For almost complex structures, the existence of a splitting is equivalent to the existence of local coordinates in which the almost complex structure can be represented by a purely numerical matrix, i.e. containing no Grassmann variables. For Riemannian metrics, terms up to degree 2 are allowed in such a local matrix representation, in order to preserve non-degeneracy. It is further shown that non-split structures appear in the almost complex case as deformations of a split reduction and in the Riemannian case as the deformation of an underlying metric. In contrast to non-split deformations of complex supermanifolds, these deformations can be restricted by cut-off functions to local deformations. A class of examples of nowhere split structures constructed from almost complex manifolds of dimension $6$ and higher, is provided for both cases. (English) |
| Keyword:
|
supermanifold |
| Keyword:
|
almost complex structure |
| Keyword:
|
Riemannian metric |
| Keyword:
|
non-split |
| MSC:
|
32Q60 |
| MSC:
|
53C20 |
| MSC:
|
58A50 |
| idZBL:
|
Zbl 07144738 |
| idMR:
|
MR4038358 |
| DOI:
|
10.5817/AM2019-4-229 |
| . |
| Date available:
|
2019-10-30T08:53:41Z |
| Last updated:
|
2020-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147876 |
| . |
| Reference:
|
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