On quasi-Eienstein Finsler spaces

2014/06/01 by Behroz Bidabad, Bidabad, Behroz, Mohamad Yarahmadi +1
Mathematics · #53C44 #53C60 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C44 #msc:53C60

paper · pdf · doi:10.48550/arxiv.1406.0135

To appear in Bulletin of Iranian Mathematical Society, 2014

arxiv created 2014/06/01 · arxiv updated 2014/06/03

Abstract

The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces. Quasi-Einstein metrics serve also as solution to the Ricci flow equation. Here, the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is defined. In compact case, it is proved that the quasi-Einstein metrics are solution to the Finslerian Ricci flow and conversely, certain form of solutions to the Finslerian Ricci flow are quasi-Einstein Finsler metrics.

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