Comptes Rendus
no. 11
Differential geometry
On compact Ricci solitons in Finsler geometry
[Sur les solitons de Ricci compacts en géométrie finslérienne]

Présenté par : the Editorial Board

Mohamad Yar Ahmadi1 ; Behroz Bidabad1
1 Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1023-1027.

Les solitons de Ricci sur les espaces de Finsler, précédemment définis et étudiés par les auteurs de la présente note, sont une généralisation des espaces d'Einstein, et peuvent être considérés comme des solutions du flot de Ricci sur les variétés finslériennes compactes. Dans ce travail, on démontre qu'un soliton de Ricci complet contractant en temps croissant sur un espace de Finsler est compact si et seulement s'il est borné. En outre, il est démontré qu'un soliton de Ricci contractant compact donne lieu à un groupe fondamental de type fini et donc que le premier groupe de cohomologie s'annule.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.09.012
Mohamad Yar Ahmadi 1 ; Behroz Bidabad 1

1 Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran 
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Mohamad Yar Ahmadi; Behroz Bidabad. On compact Ricci solitons in Finsler geometry. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1023-1027. doi : 10.1016/j.crma.2015.09.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.012/

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