Article (Scientific journals)
Riemannian Structures on Z 2 n -Manifolds
BRUCE, Andrew; Grabowski, Janusz
2020In Mathematics, 8 (9), p. 1469
Peer reviewed
 

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Abstract :
[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
Disciplines :
Mathematics
Author, co-author :
BRUCE, Andrew ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Grabowski, Janusz;  Polish Academy of Sciences > Institute of Mathematics
External co-authors :
yes
Language :
English
Title :
Riemannian Structures on Z 2 n -Manifolds
Publication date :
September 2020
Journal title :
Mathematics
Publisher :
MDPI
Special issue title :
Geometric Methods and their Applications
Volume :
8
Issue :
9
Pages :
1469
Peer reviewed :
Peer reviewed
Name of the research project :
2016/22/M/ST1/0054
Funders :
Polish National Science Centre
Available on ORBilu :
since 16 December 2020

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