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On the gradient Finsler Yamabe solitons | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 9، دوره 1، شماره 2، آذر 2020، صفحه 229-233 اصل مقاله (304.27 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2020.18420.1034 | ||
| نویسنده | ||
| Mohamad Yar Ahmadi* | ||
| Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Finsler metric؛ gradient Yamabe soliton؛ Finite topological type | ||
| مراجع | ||
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[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). | ||
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