Tbilisi Mathematical Journal

On algebraic solitons for geometric evolution equations on three-dimensional Lie groups

Thomas H. Wears

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Abstract

The relationship between algebraic soliton metrics and self-similar solutions of geometric evolution equations on Lie groups is investigated. After discussing the general relationship between algebraic soliton metrics and self-similar solutions to geometric evolution equations, we investigate the cross curvature flow and the second order renormalization group flow on simply-connected, three-dimensional, unimodular Lie groups, providing a complete classification of left invariant algebraic solitons that give rise to self-similar solutions of the corresponding flows on such spaces.

Article information

Source
Tbilisi Math. J., Volume 9, Issue 2 (2016), 33-58.

Dates
Received: 13 October 2015
Accepted: 30 July 2016
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769066

Digital Object Identifier
doi:10.1515/tmj-2016-0018

Mathematical Reviews number (MathSciNet)
MR3555190

Zentralblatt MATH identifier
1350.53087

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 58B20: Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]

Keywords
Geometric evolution equations soliton metrics algebraic soliton metrics Lie groups

Citation

Wears, Thomas H. On algebraic solitons for geometric evolution equations on three-dimensional Lie groups. Tbilisi Math. J. 9 (2016), no. 2, 33--58. doi:10.1515/tmj-2016-0018. https://projecteuclid.org/euclid.tbilisi/1528769066


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