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Abstract
Finsler geometry is originated from Differential geometry. Finsler geometry is Riemannian metric without quadratic restriction. In Finsler space we see special metrics such as Randers metric, Kropina metric and Matsumoto metric.,etc. Projective change between two Finsler metrics arise from Information Geometry. Such metrics have special geometric properties and will play an important role in Finsler geometry. In this paper,we are going to study class of Projective change between two s, which are defined as the sum of a Riemannian metric and .
Keywords: Finsler metric, Special Finsler metric, , Douglas Space, Geodesic, Spray coefficients, Projectively related metric, Projective change between two metrics##plugins.themes.academic_pro.article.details##
How to Cite
K, G., & S.K, N. (2015). Projective Change between Special (α,β)- Finsler Metric and Rander’s Metric. International Journal of Emerging Trends in Science and Technology, 2(01). Retrieved from https://igmpublication.org/ijetst.in/index.php/ijetst/article/view/468
References
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S. Bacso and M. Matsumoto, Projective change between Finsler spaces with (α,β)-metric, Tensor N. S., 55(1994), 252-257.
S. Bacso, X. Cheng and Z. Shen, Curvature Properties of (α,β)-metrics, Adv. Stud. Pure Math. Soc.,Japan (2007).
Chern S.S and Z.Shen, Riemann-Finsler Geometry, World Scientific Publishing Co. Pte. Ltd., Hackensack,NJ, 2005.
X.Cheng and Z. Shen, A Class of Finsler metrics with isotropic S-curvature, Israel J. Math., 169(2009), 317-340.
Ningwei Cui and Yi-Bing Shen, Projective change between two classes of (α,β)-metrics, Diff. Geom. And its Applications, 27 (2009), 566-573.
H. S. Park and II-Yong Lee, On Projectively flat Finsler spaces with (α,β)-metric, Comm. Korean Math. Soc., 14(2)(1999), 373-383.
H. S. Park and II-Yong Lee, The Randers changes of Finsler spaces with (α,β)-metrics of Douglas type, Comm. Korean Math. Soc., 38(3)(2001), 503-521.
H. S. Park and II-Yong Lee, Projective changes between a Finsler space with (α,β)-metric and associated Riemannian metric, Canad. J. Math., 60(2008), 443-456.
Pradeep Kumar, S.K. Narasimhamurthy, H.G. Nagaja and S.T. Aveesh, On a special hypersurface of a Finsler space with (α,β)-metric, Tbilisi Mathematical Journal, 2(2009), 51-60.
B.N. Prasad, B.N Gupta and D.D. Singh, Conformal transformation in Finsler spaces with (α,β)-metric, Indian J. Pure and Appl. Math., 18(4)(1961), 290-301.
M. Matsumoto and X. Wei, Projective changes of Finsler spaces of constant curvature, Publ. Math. Debreen, 44(1994), 175-181
B. Nafaji, Z.Shen and A. Tayebi, Finsler metircs of scalar flag curvature with special non-Riemannian curvature properties, J.Geom. Dedicata., 131 (2008), 87-97.
S. Bacso and M. Matsumoto, Projective change between Finsler spaces with (α,β)-metric, Tensor N. S., 55(1994), 252-257.
S. Bacso, X. Cheng and Z. Shen, Curvature Properties of (α,β)-metrics, Adv. Stud. Pure Math. Soc.,Japan (2007).
Chern S.S and Z.Shen, Riemann-Finsler Geometry, World Scientific Publishing Co. Pte. Ltd., Hackensack,NJ, 2005.
X.Cheng and Z. Shen, A Class of Finsler metrics with isotropic S-curvature, Israel J. Math., 169(2009), 317-340.
Ningwei Cui and Yi-Bing Shen, Projective change between two classes of (α,β)-metrics, Diff. Geom. And its Applications, 27 (2009), 566-573.
H. S. Park and II-Yong Lee, On Projectively flat Finsler spaces with (α,β)-metric, Comm. Korean Math. Soc., 14(2)(1999), 373-383.
H. S. Park and II-Yong Lee, The Randers changes of Finsler spaces with (α,β)-metrics of Douglas type, Comm. Korean Math. Soc., 38(3)(2001), 503-521.
H. S. Park and II-Yong Lee, Projective changes between a Finsler space with (α,β)-metric and associated Riemannian metric, Canad. J. Math., 60(2008), 443-456.
Pradeep Kumar, S.K. Narasimhamurthy, H.G. Nagaja and S.T. Aveesh, On a special hypersurface of a Finsler space with (α,β)-metric, Tbilisi Mathematical Journal, 2(2009), 51-60.
B.N. Prasad, B.N Gupta and D.D. Singh, Conformal transformation in Finsler spaces with (α,β)-metric, Indian J. Pure and Appl. Math., 18(4)(1961), 290-301.
M. Matsumoto and X. Wei, Projective changes of Finsler spaces of constant curvature, Publ. Math. Debreen, 44(1994), 175-181
B. Nafaji, Z.Shen and A. Tayebi, Finsler metircs of scalar flag curvature with special non-Riemannian curvature properties, J.Geom. Dedicata., 131 (2008), 87-97.