On Special Spaces of Torsion Tensor in Generalized  Recurrent Finsler Space

Alaa A Abdallah; Ahmed A  Hamoud; A A Navlekar; Kirtiwant P  Ghadle

doi:10.48165/

Authors

Alaa A Abdallah Department of Mathematics, Abyan University, Abyan, Yemen
Ahmed A Hamoud Department of Mathematics, Taiz University, Taiz- 96704, Yemen.
A A Navlekar Department of Mathematics, Pratishitan Mahavidyalaya, Paithan (M.S.) India.
Kirtiwant P Ghadle Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India.

DOI:

https://doi.org/10.48165/

Keywords:

like space, reducible space, semi reducible space

Abstract

The purpose of the present paper is to use the properties of like space, reducible space, semi reducible space and like space in the generalized recurrent space to get new spaces related to generalized recurrent. Further, we find certain identities belong to these spaces.

References

Abdallah A. A., Navlekar A. A. and Ghadle K. P. (2019). On study generalized recurrent Finsler space, International Journal of Mathematics trends and technology, 65(4), 74-79.

Abdallah A. A., Navlekar A. A. and Ghadle K. P. (2019). The necessary and sufficient condition for some tensors which satisfy a generalized recurrent Finsler space, International Journal of Scientific and Engineering Research, 10 (11), 135-140.

Abdallah A. A., Navlekar A. A. and Ghadle K. P. (2019). On and reducible of Cartan's second curvature tensor, Journal of Applied Science and computation, 6(11), 13-24.

Abdallah A. A., Navlekar A. A., Ghadle K. P. and Hamoud A. A. (2022). Decomposition for Cartan’s second curvature tensor of different order in Finsler spaces, Nonlinear Functional Analysis and Applications, 27 (2), 433-448.

Tayebi and Peyghan E. (2012). On like Finsler metrics, Iranian Journal of Mathematical Sciences and Informatics, 7 (1), 1-6.

Heydari. (2020). On semi reducible Finsler spaces, Journal of Finsler Geometry and its Applications, 1 (2), 130-142.

Chethana C. and Narasimhamurthy S. K. (2015). On semi reducible Finsler metrics, Journal on Science Engineering and Technology, 2 (4), 261-264.

Prasad N. (1988). On like Finsler spaces, Indian J. Pure Appl. Math., 19, 423-428. 9. Tiwari, R. Gangopadhyay and Prajapati G. K. (2019). On semi reducibility of general Finsler metrics, Kyungpook Mathematical Journal, 59 (2), 353-362.

Rund H. (1981). The differential geometry of Finsler spaces, Springer-Verlag, Berlin Göttingen, (1959); 2nd Edit. (in Russian), Nauka, (Moscow), (1981).

Nasr K. S. (2016). Certain types of generalized tensors for third order, M.Sc. Thesis, University of Aden, (Aden), (Yemen.

Matsumoto M. (1971). On Finsler spaces with curvature tensor of some special forms, Tensor N.S., (22), 201-204.

Matsumoto M. (1971). On isotropic and recurrent Finsler, J. Math. Kyoto Univ., (11), 1-9.

Matsumoto M. and Numata S. (1980). On semi reducible Finsler spaces with constant coefficient and like Finsler spaces, Tensor, 34 (2), 218-222.

Dwivedi P. K. (2011). reducible Finsler spaces and applications, int. journal of Math. Analysis, 5 (5), 223-229.

Saxena P. S. (2013). A study of reducible Finsler space with Douglas tensor, Journal of International Academy of physical Science, 17 (3), 277-285.

Gangopadhyay R. and Tiwari B. (2021). On likeFinsler metrics under Ricci flow, Bulletin of the Transilvania University of Brasov Series III - Mathematics and Computer Science, (2021), 1-8. 18. Beizavi S. (2020). On reducible Finsler manifolds, Journal of Finsler Geometry and its Applications, 1 (2), 73-82.

Aveesh S. T., Kumar P., Nagaraja H. G. and Narasimhamurthy S. K. (2009). Special form of Rund’s curvature tensor using like Finsler space, Journal of Generalized Lie Theory and Applications, 3(3), 175–180.

Pandey T. N. and Tripathi B. K. (2007). Four dimenstonal like Finsler space, Tensor. New series, 68 (2), 130-134.

Singh U. P. and Gupta B. N. (1985). Hypersurfaces of like Finsler spaces, Publications de L'institut Mathematique Nouvelle serie, tome, 38 (52), 177-182.