Complete Ricci solitons on Finsler manifolds
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The geometric flow theory and its applications turned into one of the most intensively developing branches of modern geometry. Here, a brief introduction to Finslerian Ricci flow and their self-similar solutions known as Ricci solitons are given and some recent results are presented. They are a generalization of Einstein metrics and are previously developed by the present authors for Finsler manifolds. In the present work, it is shown that a complete shrinking Ricci soliton Finsler manifold has a finite fundamental group.
Keywordsquasi-Einstein shrinking Finsler metric Ricci soliton Ricci flow
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The second author thanks School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran for the support.