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Complete Ricci solitons on Finsler manifolds

  • Behroz Bidabad
  • Mohamad Yar Ahmadi
Articles

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.

Keywords

quasi-Einstein shrinking Finsler metric Ricci soliton Ricci flow 

MSC(2010)

53C60 53C44 

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Notes

Acknowledgements

The second author thanks School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran for the support.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran

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