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Journals / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2017 / Cilt: 7 - Sayı: 2

NONHOLONOMIC FRAMES FOR FINSLER SPACE WITH DEFORMED MATSUMOTO METRIC

V. K. CHAUBEY
BRIJESH KUMAR TRIPATHI
Pages
337–342
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

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Objective & Hypothesis:The purpose of present paper is to find the nonholonomic frames for the deformed Matsumoto type metric which are given in the forms I. ( α2 α−β )α = α3 α−β II. ( α2 α−β )β = α2β α−β where α2 = aij (x)yi yj and β = bi(x)yi .
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Key Findings & Data:The purpose of present paper is to find the nonholonomic frames for the deformed Matsumoto type metric which are given in the forms I. ( α2 α−β )α = α3 α−β II. ( α2 α−β )β = α2β α−β where α2 = aij (x)yi yj and β = bi(x)yi .
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

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. ( α2 α−β )α = α3 α−β II. ( α2 α−β )β = α2β α−β where α2 = aij (x)yi yj and β = bi(x)yi . 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.

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Cite This Article

CHAUBEY, V. K., TRIPATHI, B. K. (2017). NONHOLONOMIC FRAMES FOR FINSLER SPACE WITH DEFORMED MATSUMOTO METRIC. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 7 - Sayı: 2, 337–342. https://ajindex.com/articles/327521

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References (17)

  1. Holland,P.R., (1982), Electromagnetism, Particles and Anholonomy. Physics Letters, 91, 6, pp.275- 278
  2. 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
  3. Ingarden,R.S., (1987), On Physical interpretations of Finsler and Kawaguchi spaces. Tensor N.S., 46, pp.354-360
  4. Randers,G., (1941), On asymmetric metric in the four space of general relativity. Phys. Rev., 59, pp.195-199
  5. Beil,R.G., (1995), Comparison of unified field theories. Tensor N.S., 56, pp.175-183
  6. Beil,R.G., (1993), Finsler and Kaluza-Klein Gauge Theories, Intern. J. Theor. Phys., 32, 6, pp.1021- 1031
  7. Miron,R. and Anastasiei,M., (1994), The geometry of Lagrange spaces:Theory and Applications, Kluwer Acad. Publ., FTPH, no. 59
  8. Antonelli,P.L., Bucataru,I., (2001), Finsler connections in anholonomic geometry of a Kropina space. Nonlinear Studies, 8, 1, pp.171-184
  9. Hrimiuc,D., Shimada,H., (1996), On the L-duality between Lagrange and Hamilton manifolds. Nonlinear World, 3, pp.613-641
  10. Ioan Bucataru, Radu Miron, (2007), Finsler-Lagrange Geometry. Applications to dynamical systems CEEX ET 3174/2005-2007, and CEEX M III 12595/2007
  11. Matsumoto,M., (1992), Theory of Finsler spaces with (α, β)-metric, Rep. Math. Phys., 31, pp.43-83
  12. Bucataru,I., (2002), Nonholonomic frames on Finsler geometry. Balkan Journal of Geometry and its Applications, 7, 1, pp.13-27
  13. Matsumoto,M., (1986), Foundations of Finsler geometry and special Finsler spaces, Kaishesha Press, Otsu, Japan
  14. 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
  15. 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 Publications, 4, 1, pp.1-7
  16. 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
  17. Erdelyi,A., (1956), Asymptotic expansions, Dover publications, New York.