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arXiv · 1508.02148

On compact Ricci solitons in Finsler geometry

Behroz Bidabad·Mohamad Yar Ahmadi
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Abstract

Ricci solitons on Finsler spaces, previously developed by the present authors, are a generalization of Einstein spaces, which can be considered as a solution to the Ricci flow on compact Finsler manifolds. In the present work it is shown that on a Finslerian space, a forward complete shrinking Ricci soliton is compact if and only if it is bounded. Moreover, it is proved that a compact shrinking Finslerian Ricci soliton has finite fundamental group and hence the first de Rham cohomology group vanishes.

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Behroz Bidabad, Mohamad Yar Ahmadi. 2015-08-10. On compact Ricci solitons in Finsler geometry. https://arxiv.org/abs/1508.02148

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