New Examples Of Shrinking Laplacian Solitons

Author:

NICOLINI MARINA1

Affiliation:

1. Universidad Nacional de Córdoba and CIEM (CONICET), Argentina

Abstract

Abstract We give a one-parameter family of examples of shrinking Laplacian solitons, which are the second known solutions to the closed G2-Laplacian flow with a finite-time singularity. The torsion forms and the Laplacian and Ricci operators of a large family of G2-structures on different Lie groups are also studied. We apply these formulas to prove that, under a suitable extra condition, there is no closed eigenform for the Laplacian on such family.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference20 articles.

1. Some remarks on G2-structures;Bryant,2005

2. Laplacian flow of closed G2-structures inducing nilsolitons;Fernández;J. Geom. Anal.,2016

3. Closed warped G2-structures evolving under the Laplacian flow;Fino;Ann. Scuola Norm. Sup. Pisa Cl. Sci.,2020

4. Closed G2-structures on non-solvable Lie groups;Fino;Rev. Mat. Complut.,2019

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