Self similar solutions of the Yamabe flow and gradient Einstein-type manifolds in the Finsler geometry

Subject Areas : هندسه

Mohamad Yar Ahmadi ¹ , Neda Izadian ² , Sina Hedayatian ³

1 - Department of Mathematics , Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz , , Ahvaz , Iran
2 - Department of Mathematics , Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz , , Ahvaz , Iran
3 - Department of Mathematics,, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, , Ahvaz, Iran

Received: 2022-05-15 Accepted : 2022-12-03 Published : 2024-01-18

Keywords: منیفلد انیشتین‌گونه, توپولوژی‌گونه متناهی, متر فینسلر, سالیتون یامابه, شار یامابه,

Abstract :

In the present work, the concepts of Finslerian Yamabe flow equation and Yamabe solitons are investigated. First of all, by using the local one-parameter group of diffeomorphism relevant to Yamabe soliton’s vector fields, we find a group of Finslerian metrics as solutions to the Finslerian Yamabe flow. In the other words, a Finslerian Yamabe soliton is a solution of the Finslerian Yamabe flow. These solutions are self-similar solutions of Finslerian Yamabe flow equation and have interesting geometric and physical properties. Furthermore, the notion of extended gradient Einstein-type manifolds is studied on Finsler spaces. Moreover, we show that by considering either the Ricci tensor is bounded from below and injectivity radius is bounded away from zero or the Ricci tensor is bounded from above, then the complete extended gradient Einstein-type Finslerian manifold is of finite topological type structure. Indeed, this manifold is homeomorghic to the interior of a compact manifold with boundary.

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