On Weekly Berwald Finsler special (α, β) - metric

  • Thippeswamy K.R Department of Mathematics, Kuvempu University, Shankaraghatta - 577451, Shimoga, Karnataka, India
  • Narasimhamurthy S. K Department of Mathematics, Kuvempu University, Shankaraghatta - 577451, Shimoga, Karnataka, India
Keywords: Isotropic Berwald curvature, S-curvature, almost isotropic flag curvature.

Abstract

In this paper we study the special (α, β)-metric F = (α2/α-β)+ β on a manifold M. We prove that F is of scalar flag curvature and isotropic Scurvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature. 

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References

S. Basco and M. Matsumoto, On Finsler spaces of Douglas type, A gen- eralization of notion of Berwald space, Publ. Math. Debrecen. 51(1997), 385-406.

D. Bao, S. S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, Springer-Verlag, 2000.

X. Chun-Huan and X. Cheng, On a class of weakly-Berwald (α, β)- metrics, J. Math. Res. Expos. 29(2009), 227-236.

X. Cheng and Z. Shen, Randers metric with special curvature properties, Osaka. J. Math. 40(2003), 87-101.

X. Cheng and Z. Shen, A class of Finsler metrics with isotropic S- curvature, Israel. J. Math. 169(2009), 317-340.

X. Chen and Z. Shen, On Douglas metrics, Publ. Math. Debrecen. 66(2005), 503-512.

X. Cheng, H. Wang and M. Wang, (α, β)-metrics with relatively isotropic mean Landsberg curvature, Publ. Math. Debrecen. 72(2008), 475-485.

N. Cui, On the S-curvature of some (α, β)-metrics, Acta. Math. Scien- tia, Series: A. 26(7) (2006), 1047-1056.

I.Y. Lee and M.H. Lee, On weakly-Berwald spaces of special (α, β)- metrics, Bull. Korean Math. Soc. 43(2) (2006), 425-441.

M. Matsumoto, Theory of Finsler spaces with (α, β)-metric, Rep. Math. Phys. 31(1992), 43-84.

S. K. Narasimhamurthy, A.R. Kavyashree and Y. Mallikarjun, Curvature properties of homogeneous matsumato metric, in press.

S. K. Narasimhamurthy, A.R. Kavyashree, Ajith and Y. Mallikarjun, On a Class of Weakly Berwald (α, β)-metrics of Scalar flag curvature, in press.

B. Najafi, Z. Shen and A. Tayebi , Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties, Geom. Dedicata. 131(2008), 87-97.

H. S. Park and E. S. Choi, On a Finsler spaces with a special (α, β)- metric, Tensor, N. S. 56(1995),142-148.

H. S. Park and E. S. Choi, Finsler spaces with an approximate Mat- sumoto metric of Douglas type, Comm. Korean. Math. Soc. 14(1999), 535-544.

H. S. Park and E. S. Choi, Finsler spaces with the second approximate Matsumoto metric, Bull. Korean. Math. Soc. 39(1) (2002), 153-163.

H. S. Park, I. Y. Lee and C. K. Park, Finsler space with the gen- eral approximate Matsumoto metric, Indian J. Pure. Appl. Math. 34(1) (2002), 59-77.

H. S. Park, I.Y. Lee, H. Y. Park and B. D. Kim, Projectively flat Finsler space with an approximate Matsumoto metric, Comm. Korean. Math. Soc. 18(2003), 501-513.

Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, Dordrecht, 2001.

A. Tayebi and B. Najafi, On isotropic Berwald metrics, Ann. Polon. Math. 103(2012), 109-121.

A. Tayebi, E. Peyghan and H. Sadeghi, On Matsumoto-type Finsler metrics, Nonlinear Analysis: RWA. 13(2012), 2556-2561.

A. Tayebi, E. Peyghan and H. Sadeghi, On Matsumoto-type Finsler metrics, Nonlinear Analysis: RWA. 13(2012), 2556-2561.

Published
2017-07-10
How to Cite
K.R, T., & S. K, N. (2017). On Weekly Berwald Finsler special (α, β) - metric. Journal of Progressive Research in Mathematics, 12(2), 1811-1820. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1171
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Articles