Abstract
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.
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Acknowledgements
The second author thanks School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran for the support.
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Bidabad, B., Yar Ahmadi, M. Complete Ricci solitons on Finsler manifolds. Sci. China Math. 61, 1825–1832 (2018). https://doi.org/10.1007/s11425-017-9349-8
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DOI: https://doi.org/10.1007/s11425-017-9349-8