Locally Conformally Flat Lorentzian Gradient Ricci Solitons

2011/06/15 by Miguel Brozos‐Vázquez, Brozos-Vázquez, M., Eduardo García‐Río +3
Mathematics · Physics and Astronomy · #53C21 #53C25 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1106.2924

openalex publication_date 2011/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that locally conformally flat Lorentzian gradient Ricci solitons are locally isometric to a Robertson-Walker warped product, if the gradient of the potential function is non null, and to a plane wave, if the gradient of the potential function is null. The latter gradient Ricci solitons are necessarily steady.

Citations

• A curvature condition for a twisted product¶to be a warped product

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