Non-split almost complex and non-split Riemannian supermanifolds
Differential Geometry
2015-01-29 v1
Abstract
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. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the second 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.
Cite
@article{arxiv.1501.07117,
title = {Non-split almost complex and non-split Riemannian supermanifolds},
author = {Matthias Kalus},
journal= {arXiv preprint arXiv:1501.07117},
year = {2015}
}