On the gradient Finsler Yamabe solitons

Document Type : Original Article

Author

Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

Here, it is proved that the potential functions of Finsler Yamabe solitons have at most quadratic growth in distance function. Also it is obtained a finite topological type property on complete gradient Finsler Yamabe solitons under suitable scalar curvature assumptions.

Keywords

Main Subjects


[1] D. Bao, S. S. Chern, Z. Shen, An Introduction to Riemann-Finsler Geometry, Graduate Texts in Mathematics, vol. 200, Springer, 2000.
[2] B. Bidabad, A. Shahi, On Sobolev spaces and density theorems on Finsler manifolds, AUT J. Math. Com., 1(1) (2020) 37-45.
[3] B. Bidabad, M. Yar Ahmadi, On complete Finslerian Yamabe solitons, Differential Geometry and its Applications, 66 (2019) 52-60.
[4] B. Bidabad, M. Yar Ahmadi, On complete Yamabe solitons, Advances in Geometry, 18 (1) (2018) 101-104.
[5] B. Bidabad, M. Yar Ahmadi, Complete Ricci solitons on Finsler manifolds, Sci. China Math, 61 (2018) 1825- 1832.
[6] B. Bidabad, A. Shahi, M. Yar Ahmadi, Deformation of Cartan curvature on Finsler manifolds, Bull. Korean Math. Soc., 54 (2017) 2119-2139.
[7] B. Bidabad, M. Yar Ahmadi, On quasi-Einstein Finsler spaces, Bull Iranian Math. Soc., 40 (2014) 921-930.
[8] F. Q. Fang, J. W. Man, Z .L. Zhang, Complete gradient shrinking Ricci solitons have finite topological type, Comptes Rendus Mathematique 346 (2008) 653-656.
[9] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Diffl. Geom, 17 (1982) no. 2, 255-306.
[10] Z. Shen, On complete manifolds of nonnegative kth-Ricci curvature, Transactions of the American Mathematical Society, 338(1) (1993) 289-310.
[11] J. Y. Wu, On a class of complete non-compact gradient Yamabe solitons, arXiv preprint, arXiv: 1109.0861 (2011).