Title of article :
The Long-Time Existence of the Finslerian Ricci Flow
Author/Authors :
Yar Ahmadi ، Mohamad Department of Mathematics - Faculty of Mathematical Sciences and Computer - Shahid Chamran University of Ahvaz , Bidabad ، Behroz Department of Mathematics - Faculty of Mathematics and Computer Science - Amirkabir University of Technology , Shahi ، Alireza Department of Mathematics - Faculty of Mathematics and Computer Science - Amirkabir University of Technology
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.
Keywords :
Finsler manifold , Long , time existence , Finslerian Ricci flow , Evolution equation , Blow , up
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
