Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran. E-mail: azami@sci.ikiu.ac.ir, shahrood78@gmail.com
In this paper, we study Ricci-Bourguignon soliton on Finsler manifolds and prove any forward complete shrinking Finslerian Ricci-Bourguignon soliton under some conditions on vector filed and scalar curvature is compact and its fundamental group is finite.
1. H. Akbar-Zadeh, Initiation to global Finslerian geometry, Netherlands: Elsevier Science, 2006.
2. M. Anastasiei, A generalization of Myers theorem, An. Stiint. Univ. ”Al. I. Cuza” Din Iasi (S.N.) Math. LIII (Supliment)(2007), 33-40.
3. 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.
4. S. Azami and A. Razavi, Yamabe flow on Berwald manifolds, Int. J. Geom. Methods Mod. Phys., 12 (2015), 27 pp.
5. D. Bao, On two curvature-driven problems in Riemann-Finsler geometry, Finsler geometry, Sapporo 2005-in memory of Makoto Matsumoto, 19C71, Adv. Stud. Pure Math.,48, Math. Soc. Japan, Tokyo, 2007.
6. D. Bao, S. Chern and Z. Shen, An introduction to Riemannian Finsler geometry, Springer-Verlag, 2000.
7. B. Bidabad and M. K. Sedaghat, Ricci flow on Finsler surfaces, J. Geom. Phys. 129(2018), 238-254.
8. B. Bidabad and M. Yar Ahmadi, On quasi-Einstein Finsler spaces, Bull. Iranian Math. Soc. 40(2014), 921-930.
9. B. Bidabad and M. Yar Ahmadi, On complete Finslerian Yamabe solitons, Differ. Geom. Appl. 66(2019), 52-60.
10. B. Bidabad and M. Yar Ahmadi, Complete Ricci solitons on Finsler manifolds, Science China Mathematics, 61(10)(2018), 1825-1832.
11. A. M. Blaga and H. M. Tastan, Some results on almost η-Ricci-Bourguignon soliton, Journal of geometry and physics, 168(2021), 104316.
12. J. P. Bourguignon, Ricci curvature and Einstein metrics, Global differential geometry and global analysis (Berlin,1979) Lecture nots in Math. vol. 838, Springer, Berlin, 1981, 42-63.
13. G. Catino, L. Cremaschi, Z. Djadli, C. Mantegazza and L. Mazzieri, The RicciBourguignon flow, Pacific J. Math. 287(2)(2015), 337-370.
14. G. Catino, L. Mazzieri and S. Mongodi, Rigidity of gradient Einstein shrinkers, Communications in Contemporay Mathematics. 17(6)(2015), 1550046 (18 pages).
15. S. Dwivedi, Some results on Ricci-Bourguignon solitons and almost solitons, Canadian Mathematical Bulletin, (2020), 1-14.
16. R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry, 17 (2)(1982), 255-306.
17. R.S. Hamilton, The Ricci flow on surfaces, Math. and general relativity (Santa Cruz, CA, 1986), Contemp. Math. 71(1988) 237-262.
18. Z. M. Shen, Lectures on Finsler geometry, World Scientific publishing Co.2001, Indiana Univ. Math. J. 26 (1977), 459-472.
19. M. Yar Ahmadi and B. Bidabad, On compact Ricci solitons in Finsler geometry, C. R. Acad. Sci. Paris Ser. I. 353(2015), 1023-1027.
Azami, S. (2021). Complete Ricci-Bourguignon solitons on Finsler manifolds. Journal of Finsler Geometry and its Applications, 2(1), 108-117. doi: 10.22098/jfga.2021.1268
MLA
Shahroud Azami. "Complete Ricci-Bourguignon solitons on Finsler manifolds", Journal of Finsler Geometry and its Applications, 2, 1, 2021, 108-117. doi: 10.22098/jfga.2021.1268
HARVARD
Azami, S. (2021). 'Complete Ricci-Bourguignon solitons on Finsler manifolds', Journal of Finsler Geometry and its Applications, 2(1), pp. 108-117. doi: 10.22098/jfga.2021.1268
VANCOUVER
Azami, S. Complete Ricci-Bourguignon solitons on Finsler manifolds. Journal of Finsler Geometry and its Applications, 2021; 2(1): 108-117. doi: 10.22098/jfga.2021.1268
)