l2c=β"> 2C=β."> L2C=β">

Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 14 (2019), 141 -- 147

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ON FINSLER SPACES WITH UNIFIED MAIN SCALAR L2C=β

Brijesh Kumar Tripathi and Pradeep Kumar

Abstract. The purpose of present paper is to study the T-tensor of such a Finsler space with the condition L2(α,β)C=β, where α=sqrt(aij(x)yiyj) and β=biyi and get some important theorems. We shall also obtain the condition for such a Finsler space to be a Landsberg space or Berwald space. The notations and terminologies are referred to the monograph [7].

2010 Mathematics Subject Classification: 53C60;53B40.
Keywords: Finsler space; T-tensor; unified scalar; L2C=β.

Full text

References

  1. G. S. Asanov and E. G. Kirnasov, On Finsler spaces satisfying T- Condition, Aequ. Math. Univ. of Waterloo, 24 (1982), 66-73. MR0698117. Zbl 0507.53024.

  2. P. L. Antonelli, Handbook of Finsler geometry, Kluwer Academic Publishers, Netherlands, 1993. MR2067663. Zbl 1057.53001.

  3. P. L. Antonelli, R. S. Ingarden,and M. Matsumoto, The theory of sprays and Finsler spaces with applications in physics and biology, Kluwer Academic Publishers, Dordrecht, 1993. MR1273129. Zbl 0821.53001.

  4. F. Ikeda,On Finsler spaces satisfying the condition L2C2=f(x), An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat., 30(1984), no. 4, 31-33. MR0799960. Zbl 0577.53024.

  5. F. Ikeda, On the tensor Tijkl of Finsler spaces, Tensor (N. S.) 33(1979), 203-209. MR0577427. Zbl 0439.53039.

  6. M. Matsumoto, On C-reducible Finsler space, Tensor (N. S.), 24(1972), 29-37. MR0326608. Zbl 0246.53057.

  7. M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha Press, Saikawa, Otsu, Japan, 1986. MR0858830. Zbl 0594.53001.

  8. M. Matsumoto and S. Numata, On semi C-reducible Finsler spaces with constant coefficients and C2-like Finsler spaces, Tensor (N. S.), 34(1980) 218-222. MR0578985. Zbl 0435.53023.

  9. M. Matsumoto and C. Shibata,On semi-C-reducibility, T-tensor = 0 and S4-likeness of Finsler spaces, J. Math. Kyoto Univ., 19(1979), 301-314. MR0545711. Zbl 0417.53015.

  10. T. N. Pandey, V. K. Chaubey and Arunima Mishra, On Finsler Spaces with unified main scalar (LC) of the form L2C2=f(y)+ g(x), International J. Math. Combin, 1(2012) 41 - 46. Zbl 1329.53039.

  11. B. Tiwari, Landsberg spaces satisfying semi-T'-condition, Differential Geometry-Dynamical Systems, 12(2010), 246-251. MR2606566. Zbl 1200.53022.



Brijesh Kumar Tripathi
Department of Mathematics, L.D. College of Engineering Ahmedabad,
Navrangpura, Ahmedabad, Gujarat, 380015, India.
E-mail: brijeshkumartripathi4@gmail.com, drbrijeshtripathi@ldce.ac.in

Pradeep Kumar
Department of Mathematics, Digvijaynath P.G. College Gorakhpur,
Uttar Pradesh, 273001, India.
E-mail: pradeepshuklamath@gmail.com

http://www.utgjiu.ro/math/sma