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arXiv · 1507.03785

Convergence of Finslerian metrics under Ricci flow

M. Yar Ahmadi·B. Bidabad
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Abstract

In this work, convergence of evolving Finslerian metrics first in a general flow next under Finslerian Ricci flow is studied. More intuitively it is proved that a family of Finslerian metrics $g(t)$ which are solutions to the Finslerian Ricci flow converge in $C^{\infty}$ to a smooth limit Finslerian metric as $ t $ approaches the finite time $ T $. As a consequence of this result one can show that in a compact Finsler manifold the curvature tensor along Ricci flow blows up in short time.

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BibTeXRIS

M. Yar Ahmadi, B. Bidabad. 2015-07-14. Convergence of Finslerian metrics under Ricci flow. https://doi.org/10.1007/s11425-015-5092-3

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