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The Long-Time Existence of the Finslerian Ricci Flow

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Abstract

In this study, we demonstrate that any solution to the Finslerian Ricci flow encountering a singularity on a compact manifold is invariably associated with an unbounded hh-curvature tensor. Furthermore, we establish the extended temporal viability of the Finslerian Ricci flow under the constraint of bounded curvature. To achieve this, we derive the evolution equation for the hh-curvature tensor and establish precise estimates for the covariant derivatives of the Cartan curvature tensor.

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Acknowledgements

The first author is grateful to the Research Council of Shahid Chamran University of Ahvaz (Ahvaz-Iran) for financial support (Grant Number: SCU.MM1402.47684).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Golestan Blvd, 61357, Ahvaz, Iran

    Mohamad Yar Ahmadi

  2. Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Hafez av., 15916, Tehran, Iran

    Behroz Bidabad & Alireza Shahi

  3. Institut de Mathematique de Toulouse, Universite’ Paul Sabatier, 118 route de Narbonne, F-31062, Toulouse, France

    Behroz Bidabad

Authors
  1. Mohamad Yar Ahmadi
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  2. Behroz Bidabad
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  3. Alireza Shahi
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Correspondence to Mohamad Yar Ahmadi.

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Communicated by Mohammad Reza Koushesh.

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Yar Ahmadi, M., Bidabad, B. & Shahi, A. The Long-Time Existence of the Finslerian Ricci Flow. Bull. Iran. Math. Soc. 50, 20 (2024). https://doi.org/10.1007/s41980-023-00857-6

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  • DOI: https://doi.org/10.1007/s41980-023-00857-6

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