Non-split almost complex and non-split Riemannian supermanifolds

2015/01/28 by Matthias Kalus, Kalus, Matthias · 1 citation
Mathematics · #32Q60 #53C20 #58A50 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:32Q60 #msc:53C20 #msc:58A50

paper · pdf · doi:10.48550/arxiv.1501.07117

arxiv created 2015/01/28 · arxiv updated 2015/01/29

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.

Cited by

• On a Grassmann odd analogue of Carrollian Manifolds

Related

• Complex supermanifolds of odd dimension beyond 5
• Non-split superstrings of dimension (1|2)
• Embeddings of Complex Supermanifolds
• Even and odd geometries on supermanifolds
• Families of Supermanifolds: Splitting Types and Obstruction Maps