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Ricci tensor in graded geometry

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2020Embargo end date: 01 Jan 2020 English Publisher:Elsevier BVJournal:Physics Letters B, volume 807, page 135,582 (issn: 0370-2693, Copyright policy )
Authors: Fridrich Valach;

doi: 10.1016/j.physletb.2020.135582 , 10.48550/arxiv.2001.03382

arXiv: 2001.03382

Ricci tensor in graded geometry

Abstract

We define the notion of the Ricci tensor for NQ symplectic manifolds of degree 2 and show that it corresponds to the standard generalized Ricci tensor on Courant algebroids. We use an appropriate notion of connections compatible with the generalized metric on the graded manifold.

6 pages, minor changes, added references, accepted manuscript version

Related Organizations
Keywords

Mathematics - Differential Geometry, High Energy Physics - Theory, Physics, QC1-999, FOS: Physical sciences, Symplectic manifolds (general theory), Mathematical Physics (math-ph), Ricci tensor, NQ manifolds, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), 53D18, General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Mathematical Physics, Courant algebroids

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green
gold