On quasi-Einstein Finsler spaces. (English) Zbl 1337.53090
Summary: 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 solutions to the Finslerian Ricci flow and conversely, certain solutions to the Finslerian Ricci flow are quasi-Einstein Finsler metrics.
MSC:
53C60 | Global differential geometry of Finsler spaces and generalizations (areal metrics) |
53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
35C08 | Soliton solutions |