Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T03:56:49.222Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of the Ricci tensor on locally homogeneous Lorentzian gradient Ricci solitons

Part of: Global differential geometry Local differential geometry

Published online by Cambridge University Press:  22 February 2018

M. Brozos-Vázquez ,
E. García-Río ,
S. Gavino-Fernández  and
P. Gilkey
M. Brozos-Vázquez
Affiliation:
Universidade da Coruña, Differential Geometry and its Applications Research Group, Escola Politécnica Superior, 15403 Ferrol, Spain (miguel.brozos.vazquez@udc.gal)
E. García-Río
Affiliation:
Faculty of Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain (eduardo.garcia.rio@usc.es; sandra.gavino@usc.es)
S. Gavino-Fernández
Affiliation:
Faculty of Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain (eduardo.garcia.rio@usc.es; sandra.gavino@usc.es)
P. Gilkey
Affiliation:
Mathematics Department, University of Oregon, Eugene, OR 97403, USA (gilkey@uoregon.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

We describe the structure of the Ricci tensor on a locally homogeneous Lorentzian gradient Ricci soliton. In the non-steady case, we show that the soliton is rigid in dimensions 3 and 4. In the steady case we give a complete classification in dimension 3.

Keywords

locally homogeneous Lorentzian manifoldCahen–Wallach spacegradient Ricci solitonharmonic Weyl tensorWalker manifoldKilling vector field

MSC classification

Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions 53B30: Lorentz metrics, indefinite metrics 53C24: Rigidity results 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 3 , June 2018 , pp. 461 - 482
Copyright
Copyright © Royal Society of Edinburgh 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)