Reference : Riemannian Structures on Z 2 n -Manifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/45118
Riemannian Structures on Z 2 n -Manifolds
English
Bruce, Andrew mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Grabowski, Janusz mailto [Polish Academy of Sciences > Institute of Mathematics]
Sep-2020
Mathematics
MDPI
8
9
Geometric Methods and their Applications
1469
Yes
International
[en] Very loosely, Zn2-manifolds are ‘manifolds’ with Zn2-graded coordinates and their sign rule is determined by the scalar product of their Zn2-degrees. A little more carefully, such objects can be understood within a sheaf-theoretical framework, just as supermanifolds can, but with subtle differences. In this paper, we examine the notion of a Riemannian Zn2-manifold, i.e., a Zn2-manifold equipped with a Riemannian metric that may carry non-zero Zn2-degree. We show that the basic notions and tenets of Riemannian geometry directly generalize to the setting of Zn2-geometry. For example, the Fundamental Theorem holds in this higher graded setting. We point out the similarities and differences with Riemannian supergeometry
Polish National Science Centre
2016/22/M/ST1/0054
http://hdl.handle.net/10993/45118
10.3390/math8091469

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