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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 48 | Number 4 | Year 2017 | Article Id. IJMTT-V48P539 | DOI : https://doi.org/10.14445/22315373/IJMTT-V48P539

The Existence of Concurrent Vector Fields in a Finsler Space-I


Birendra Kumar Singh, Prakash Chandra Yadav, Ashwini Dwivedi
Abstract

In this paper a relationship between concurrent and P-concurrent vector fields in a Finsler space has been established. The present work studies the properties of concurrent vector fields [7] in Definition 1.2. Moreover, paper explains a vector field which we shall call P-concurrent vector field in a Finsler space. It generalizes the concept of concurrent vector field.

Keywords
Finsler space, concurrent vector fields, P-concurrent vector fields.
References

[1] H. Kawaguchi : On Finsler spaces with the vanishing second curvature tensor, Tensor, N.S., 26 (1972), 250-254.
[2] M. Matsumoto : On Finsler spaces with curvature tensors of some special forms, Tensor, N.S., 22 (1971), 201-204.
[3] M. Matsumoto : On C-reducible Finsler spaces, Tensor, N.S., 24 (1972), 29-37.
[4] M. Matsumoto:Finsler spaces admitting concurrent vector field, Tensor, N.S., 28 (1974), 239-249.
[5] M. Matsumoto : Foundations of Finsler geometry and spaecial Finsler spaces, Kaiseisha Press, Otsu, Japan, 1986.
[6] S.C. Rastogi and H. Kawaguchi : A geometrical meaning of the P-reducible condition in Finsler spaces, Tensor, N.S., 51 (1992), 251-256.
[7] S.C. Rastogi and A.K. Dwivedi : On the existence of current vector fields in a Finsler space, Tensor, N.S., 65 (2004), 48-54.
[8] H. Rund : The differential geometry of Finsler spaces, Springer-Verlag, 1959.
[9] S. Tachibana : On Finsler spaces which admit concurrent vector field, Tensor, N.S., 1 (1950), 1-5.

Citation :

Birendra Kumar Singh, Prakash Chandra Yadav, Ashwini Dwivedi, "The Existence of Concurrent Vector Fields in a Finsler Space-I," International Journal of Mathematics Trends and Technology (IJMTT), vol. 48, no. 4, pp. 260-269, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V48P539

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