Article Sidebar

Submitted
May 29, 2020
Accepted
July 16, 2021
Published
July 24, 2021
Download
PDF
Statistic
Read Counter : 534 Download : 370

Downloads

Download data is not yet available.

Main Article Content

Abstract

In the present paper we established some interesting results on purely Hermitian R-complex Finsler space with (α, β)-metrics, Firstly we characterize the conditions for the (α, β)-metric F = p α2 + εβ2 to be a purely Hermitian. Then determined the fundamental metric tensor, its inverse and determinent of the above metric. Further obtained Chern-Finsler connection coefficients and analysed necessary conditions under which an purely Hermitian R-complex Finsler space with (α, β)-metric to be Berwald, Kahler and strongly Kahler also given some examples.

Keywords

R-complex Finsler space Purely Hermitian metric Connection coefficients Berwald space

Article Details

How to Cite
Venkatesha, K. S., Narasimhamurthy, S. K., & Chandru, K. (2021). On Purely Hermitian R-complex Finsler Space with (α, β)-Metric. Journal of the Indonesian Mathematical Society, 27(2), 240–248. https://doi.org/10.22342/jims.27.2.929.240-248
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Abate, M. and Patrizio, G., Finsler Metrics-A Global Approach, Lecture Notes in Math., Springer-Verlag, 1994.
  2. Aikou, T., Finsler geometry on complex vector bundles, Riemann-Finsler Geometry, MSRI Publications, 50 (2004), 1-23.
  3. Aldea, N., About a special class of two dimensional complex Finsler spaces, Indian J. Pure Appl. Math., 43(2) (2012), 107-127.
  4. Aldea, N. and Cˆampean, G., On some classes of R-complex Hermitian Finsler spaces, J. Korean Math. Soc. 52 (2015), No. 3, 587-601.
  5. Aldea, N. and Munteanu, G., On complex Landsberg and Berwald spaces, Journal of Geometry and Physics, 62 (2012), No. 2, 368-38
  6. Aldea, N. and Munteanu, G., On complex Finsler spaces with Randers metrics, Journal Korean Math. Soc., 46 (2009), No. 5, 949-966.
  7. Aldea, N. and Munteanu, G., On complex Douglas spaces, Journal of Geometry and Physics, 66 (2013), 80-93.
  8. Aldea, N. and Purcaru, M., R-complex Finsler spaces with (α,β)-metric, Novi Sad J. Math., 38 (2008), No. 1, 1-9.
  9. Bao, D., Chern, S. S. and Shen, Z., An Introduction to Riemannian Finsler Geometry, Graduate Texts in Math., 200, Springer-Verlag, 2000.
  10. Chen, B. and Shen, Y., K¨ahler Finsler metrics are actually strongly Kahler, Chin. Ann. Math. Ser. B, 30 (2009), No. 2, 173-178.
  11. Chen, B. and Shen, Y., On complex Randers metrics, Int. J. Math., 21(8) (2010), 971-986.
  12. Kobayashi, S., Complex Finsler vector bundles, Contemporary Math., (1996), 145-153.
  13. Matsumoto, M., Theory of Finsler space with (α, β)-metric, Rep. on Math. Phys., 31 (1991), 43-83.
  14. Munteanu, G., Complex Spaces in Finsler, Lagrange and Hamilton Geometries, Kluwer Acad. Publ., 141 FTPH, 2004.
  15. Munteanu, G. and Purcaru, M., On R- complex Finsler spaces, Balkan J. Geom. Appl., 14 (2009), No. 1, 52-59.
  16. Purcaru, M., On R-complex Finsler spaces with Kropina metric, Bull. of the Transilvania Univ. of Brasov, 4(53), (2011), No. 2, 79-88.
  17. Rizza, G. B., Stutture di Finsler di tipo quasi Hermitiano, Riv. Mat. Univ. Parma, 4 (1963), 83-106.
  18. Shen, Z., Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, Dordrecht, 2001.
  19. Venkatesha, K. S., Narasimhamurthy, S. K., and Roopa, M. K., On Hermitian R-complex Finsler spaces with special (α, β)-metric, JP Journal of Geometry and Topology, 23, (2019), No. 2, 107-127.
  20. Venkatesha, K. S. and Narasimhamurthy, S. K., On complex Finsler space with infinite series of (α, β)-metric, J. Math. Comput. Sci., 11 (2021), No. 1, 839-855