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arXiv.org e-Print Archive
Preprint . 2022
Data sources: arXiv.org e-Print Archive
https://dx.doi.org/10.48550/ar...
Article . 2022
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Symmetry breaking in geometry

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2022Embargo end date: 01 Jan 2022Publisher:arXivFunded by:FWF | Non-rigidity and symmetry...
Authors: Fuchs, Andreas; Hertrich-Jeromin, Udo; Pember, Mason;

doi: 10.48550/arxiv.2206.13401

arXiv: http://arxiv.org/abs/2206.13401

Symmetry breaking in geometry

Abstract

A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how spontaneous symmetry breaking may occur, and it is discussed how explicit symmetry breaking may be used to tackle certain geometric problems. A systematic study of symmetry breaking in geometry is proposed, and some preliminary thoughts on further research are formulated.

17 pages, 3 figures

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), 53A10 (Primary) 53A40, 53A70, 37K35, 70H33 (Secondary), FOS: Mathematics

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citations
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!
0
Average
Average
Average
Green