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NONHOLONOMIC FRAMES FOR FINSLER SPACE WITH DEFORMED MATSUMOTO METRIC

Year 2017, Volume: 7 Issue: 2, 337 - 342, 01.12.2017

Abstract

The purpose of present paper is to find the nonholonomic frames for the deformed Matsumoto type metric which are given in the forms I. α 2 α−β α = α 3 α−β II. α 2 α−β β = α 2β α−β where α 2 = aij x y i y j and β = bi x y i . The first metric of the above deformation is obtained by the product of Matsumoto and Riemannian metric and second one is the product of Matsumoto and 1-form metric.

References

  • Holland,P.R., (1982), Electromagnetism, Particles and Anholonomy. Physics Letters, 91, 6, pp.275
  • Holland,P.R., (1987), Anholonomic deformations in the ether: a significance for the electrodynamic potentials. In: Hiley, B.J. Peat, F.D. (eds.), Quantum Implications. Routledge and Kegan Paul
  • London and New York, pp.295-311. Ingarden,R.S., (1987), On Physical interpretations of Finsler and Kawaguchi spaces. Tensor N.S., 46, pp.354-360.
  • Randers,G., (1941), On asymmetric metric in the four space of general relativity. Phys. Rev., 59, pp.195-199.
  • Beil,R.G., (1995), Comparison of unified field theories. Tensor N.S., 56, pp.175-183.
  • Beil,R.G., (1993), Finsler and Kaluza-Klein Gauge Theories, Intern. J. Theor. Phys., 32, 6, pp.1021
  • Miron,R. and Anastasiei,M., (1994), The geometry of Lagrange spaces:Theory and Applications
  • Kluwer Acad. Publ., FTPH, no. 59. Antonelli,P.L., Bucataru,I., (2001), Finsler connections in anholonomic geometry of a Kropina space.
  • Nonlinear Studies, 8, 1, pp.171-184. Hrimiuc,D., Shimada,H., (1996), On the L-duality between Lagrange and Hamilton manifolds. Non- linear World, 3, pp.613-641.
  • Ioan Bucataru, Radu Miron, (2007), Finsler-Lagrange Geometry. Applications to dynamical systems CEEX ET 3174/2005-2007, and CEEX M III 12595/2007.
  • Matsumoto,M., (1992), Theory of Finsler spaces with (α, β)-metric, Rep. Math. Phys., 31, pp.43-83.
  • Bucataru,I., (2002), Nonholonomic frames on Finsler geometry. Balkan Journal of Geometry and its Applications, 7, 1, pp.13-27.
  • Matsumoto,M., (1986), Foundations of Finsler geometry and special Finsler spaces, Kaishesha Press, Otsu, Japan.
  • Tripathi, Brijesh Kumar, Pandey,K.B., and Tiwari,R.B., (2016), Nonholonomic Frame for Finsler
  • Space with (α, β)-metric,International J. Math. Combin. Vol.1, pp.109-115. Narasimhamurthy,S.K., Mallikarjun,Y.Kumar, and Kavyashree,A.R., (2014), Nonholonomic Frames
  • For Finsler Space With Special (α, β)-metric, International Journal of Scientific and Research Publi- cations, 4, 1, pp.1-7. Tripathi,B.K. and Chaubey,V.K., (2016), Nonholonomic frames for Finsler space with generalized
  • Kropina metric, International Journal of Pure and Applied Mathematics, Vol.108, 4, pp.921-928, doi:10.12732/ijpam.v108i4.17.
  • Erdelyi,A., (1956), Asymptotic expansions, Dover publications, New York.
Year 2017, Volume: 7 Issue: 2, 337 - 342, 01.12.2017

Abstract

References

  • Holland,P.R., (1982), Electromagnetism, Particles and Anholonomy. Physics Letters, 91, 6, pp.275
  • Holland,P.R., (1987), Anholonomic deformations in the ether: a significance for the electrodynamic potentials. In: Hiley, B.J. Peat, F.D. (eds.), Quantum Implications. Routledge and Kegan Paul
  • London and New York, pp.295-311. Ingarden,R.S., (1987), On Physical interpretations of Finsler and Kawaguchi spaces. Tensor N.S., 46, pp.354-360.
  • Randers,G., (1941), On asymmetric metric in the four space of general relativity. Phys. Rev., 59, pp.195-199.
  • Beil,R.G., (1995), Comparison of unified field theories. Tensor N.S., 56, pp.175-183.
  • Beil,R.G., (1993), Finsler and Kaluza-Klein Gauge Theories, Intern. J. Theor. Phys., 32, 6, pp.1021
  • Miron,R. and Anastasiei,M., (1994), The geometry of Lagrange spaces:Theory and Applications
  • Kluwer Acad. Publ., FTPH, no. 59. Antonelli,P.L., Bucataru,I., (2001), Finsler connections in anholonomic geometry of a Kropina space.
  • Nonlinear Studies, 8, 1, pp.171-184. Hrimiuc,D., Shimada,H., (1996), On the L-duality between Lagrange and Hamilton manifolds. Non- linear World, 3, pp.613-641.
  • Ioan Bucataru, Radu Miron, (2007), Finsler-Lagrange Geometry. Applications to dynamical systems CEEX ET 3174/2005-2007, and CEEX M III 12595/2007.
  • Matsumoto,M., (1992), Theory of Finsler spaces with (α, β)-metric, Rep. Math. Phys., 31, pp.43-83.
  • Bucataru,I., (2002), Nonholonomic frames on Finsler geometry. Balkan Journal of Geometry and its Applications, 7, 1, pp.13-27.
  • Matsumoto,M., (1986), Foundations of Finsler geometry and special Finsler spaces, Kaishesha Press, Otsu, Japan.
  • Tripathi, Brijesh Kumar, Pandey,K.B., and Tiwari,R.B., (2016), Nonholonomic Frame for Finsler
  • Space with (α, β)-metric,International J. Math. Combin. Vol.1, pp.109-115. Narasimhamurthy,S.K., Mallikarjun,Y.Kumar, and Kavyashree,A.R., (2014), Nonholonomic Frames
  • For Finsler Space With Special (α, β)-metric, International Journal of Scientific and Research Publi- cations, 4, 1, pp.1-7. Tripathi,B.K. and Chaubey,V.K., (2016), Nonholonomic frames for Finsler space with generalized
  • Kropina metric, International Journal of Pure and Applied Mathematics, Vol.108, 4, pp.921-928, doi:10.12732/ijpam.v108i4.17.
  • Erdelyi,A., (1956), Asymptotic expansions, Dover publications, New York.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Brijesh Kumar Tripathi This is me

V. K. Chaubey This is me

Publication Date December 1, 2017
Published in Issue Year 2017 Volume: 7 Issue: 2

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