[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2019.59.2.353

On Semi C-Reducibility of General (α, β) Finsler Metrics

Tiwari, Bankteshwar (DST-CIMS, Institute of Science, Banaras Hindu University)
Gangopadhyay, Ranadip (DST-CIMS, Institute of Science, Banaras Hindu University)
Prajapati, Ghanashyam Kr. (Loknayak Jai Prakash Institute of Technology)

Publication Information

Kyungpook Mathematical Journal / v.59, no.2, 2019 , pp. 353-362 More about this Journal

Abstract

In this paper, we study general ( ${\alpha}$ , ${\beta}$ ) Finsler metrics and prove that every general ( ${\alpha}$ , ${\beta}$ )-metric is semi C-reducible but not C2-like. As a consequence of this result we prove that every general ( ${\alpha}$ , ${\beta}$ )-metric satisfying the Ricci flow equation is Einstein.

Keywords

Finsler space; general ( ${\alpha}$ , ${\beta}$ )-metric; semi C-Reducible metrics; Ricci flow equation;

Citations & Related Records

Reference

1	H. Akbar-Zadeh, Sur les espaces de Finsler a courbures sectionnelles constantes, Acad. Roy. Belg. Bull. Cl. Sci.(5), 74(1988), 281-322.
2	D. Bao, On two curvature-driven problems in Riemann-Finsler geometry, Adv. Stud. Pure Math. 48, Math. Soc. Japan, Tokyo, 2007.
3	D. Bao, S. S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, Graduate Texts in Math. 200, Springer-Verlag, New York, 2000.
4	R. Bryant, Finsler structures on the 2-sphere satisfying K = 1, Finsler geometry, 27-42, Contemp. Math. 196, Amer. Math. Soc., Providence, RI, 1996.
5	R. Bryant, Projectively flat Finsler 2-spheres of constant curvature, Selecta Math. (N.S.), 3(1997), 161-203. DOI
6	R. Bryant, Some remarks on Finsler manifolds with constant flag curvature, Houston J. Math., 28(2)(2002), 221-262.
7	S. S. Chern and Z. Shen, Riemannian-Finsler geometry, World Scientific Publisher, Singapore, 2005.
8	R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom., 17(1982), 255-306. DOI
9	R. S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom., 24(1986), 153-179. DOI
10	M. Matsumoto, On C-reducible Finsler spaces, Tensor (N.S.), 24(1972), 29-37.
11	M. Matsumoto, Theory of Finsler spaces with ( ${\alpha},{\beta}$ )-metric, Rep. Math. Phys., 31(1992), 43-83. DOI
12	M. Matsumoto and C. Shibata, On semi-C-reducibility, T-tensor and S4-likeness of Finsler spaces, J. Math. Kyoto Univ., 19(1979), 301-314. DOI
13	N. Sadeghzadeh and A. Razavi, Ricci flow equation on C-Reducible Metrics, Int. J. Geom. Methods Mod. Phys., 8(4)(2011), 773-781. DOI
14	G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:math/0211159v1 [math.DG], 11 Nov., 2002.
15	G. Perelman, Ricci flow with surgery on three manifolds, arXiv:math/0303109v1 [math.DG], 10 Mar., 2003.
16	G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three manifolds, arXiv:math/0307245v1 [math.DG], 17 Jul., 2003.
17	G. Randers, On an Asymmetrical Metric in the Four-Space of General Relativity, Phys. Rev., 59(1941), 195. DOI
18	S. F. Rutz, Symmetry in Finsler spaces, Contemp. Math., 196(1996), 289-300. DOI
19	A. Tayebi, E. Payghan and B. Najafi, Ricci Flow Equation on ( ${\alpha},{\beta}$ )-metrics, arXiv:1108.0134v1 [math.DG], 31 Jul., 2011.
20	C. Yu and H. Zhu, On a new class of Finsler metrics, Differential Geom. Appl., 29(2011), 244-254. DOI
21	Y. Q. Yun, An introduction to general relativity, Peking University Press, 1987.
22	L. Zhou, Spherically symmetric Finsler metrics in ${\mathbb{R}}^n$ , Publ. Math. Debrecen, 80(2012), 67-77.