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On projectively related Finsler gradient Ricci solitons | ||
Journal of Finsler Geometry and its Applications | ||
دوره 5، شماره 2، اسفند 2024، صفحه 30-47 اصل مقاله (300.76 K) | ||
نوع مقاله: Original Article | ||
شناسه دیجیتال (DOI): 10.22098/jfga.2024.15333.1129 | ||
نویسندگان | ||
Xinyue Cheng* ؛ Zirui Liang | ||
School of Mathematical Sciences Chongqing Normal University, Chongqing, China | ||
چکیده | ||
In this paper, we study pointwise projectively related Finsler gradient Ricci solitons. We obtain an equation that characterizes the relationship between two pointwise projectively related Finsler gradient Ricci solitons. Further, if two Finsler gradient Ricci solitons (M, F, dVF) and (M, F, dVF) satisfy some conditions, we characterize their relationships along the geodesics. In particular, if two Finsler gradient Ricci solitons are both complete, then (M, F, dVF) is expanding or shrinking and (M, F, dVF) is shrinking. | ||
کلیدواژهها | ||
Finsler metric؛ Finsler gradient Ricci soliton؛ projectively related Finsler metrics؛ S-curvature؛ weighted Ricci curvature | ||
مراجع | ||
1. S. Azami and A. Razavi, Existence and uniqueness for solutions of Ricci flow on Finsler manifolds, Int. J. Geom. Methods Mod. Phys., 10(2013),21 pp. 2. B. Bidabad and M. Yar Ahmadi, On quasi-Einstein Finsler spaces, Bull.Iranian Math. Soc., 40(2014), 921-930. 3. X. Cheng and H. Cheng, The characterizations on a class of weakly weighted Einstein-Finsler metrics, J. Geom. Anal., 33(2023), 267. 4. X. Cheng and Z. Shen, A comparison theorem on the Ricci curvature in projective geometry, Ann. Glob. Anal. Geom., 23(2)(2003), 141-155. 5. X. Cheng and Z. Shen, Some inequalities on Finsler manifolds with weighted Ricci curvature bounded below, Results Math., 77(2022), 70. 6. S.S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts in Mathematics, Vol. 6, Singapore: World Scientific, 2005. 7. R.S. Hamilton, The Ricci flow on surfaces, Contemp. Math., 71(1988), 237-261. 8. S. Ohta, Comparison Finsler Geometry, Springer Monographs in Mathe-matics, Cham: Springer, 2021. 9. A. Rapcs´ak,Uber die bahntreuen Abbildungen metrisher R¨aume, Publ. Math. Debrecen, 8(1961), 285-290. 10. Z. Shen, Volume comparison and its applications in Riemann-Finsler ge-ometry, Adv. Math., 128(2)(1997), 306-328. 11. Z. Shen, Lectures on Finsler Geometry, Singapore: World Scientific, 2001. 12. Z. Shen, On projectively related Einstein metrics in Riemann-Finsler ge-ometry, Math. Ann., 320(4)(2001), 625-647. 13. Q. Xia, Almoste Ricci solitons on Finsler spaces, preprint, 2024. 14. H. Zhu and P. Rao, Rigidity of Finsler gradient steady Ricci soliton, Calc. Var., 62(2023), 120. | ||
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