Concircular π-Vector Fields and Special Finsler Spaces

Affiliation(s)

Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt; Center for Theoretical Physics (CTP), The British University in Egypt (BUE), Cairo, Egypt.

Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt.

Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt; Center for Theoretical Physics (CTP), The British University in Egypt (BUE), Cairo, Egypt.

Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt.

ABSTRACT

The aim of the present paper is to investigate intrinsically the notion of a concircular π-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of concurrent vector field in Finsler geometry. Some properties of concircular π-vector fields are obtained. Different types of recurrence are discussed. The effect of the existence of a concircular π-vector field on some important special Finsler spaces is investigated. Almost all results obtained in this work are formulated in a coordinate-free form.

KEYWORDS

Finsler Manifold; Cartan Connection; Concurrent π-Vector Field; Concircular π-Vector Field; Special Finsler Space, Recurrent Finsler Space

Finsler Manifold; Cartan Connection; Concurrent π-Vector Field; Concircular π-Vector Field; Special Finsler Space, Recurrent Finsler Space

Cite this paper

N. Youssef and A. Soleiman, "Concircular π-Vector Fields and Special Finsler Spaces,"*Advances in Pure Mathematics*, Vol. 3 No. 2, 2013, pp. 282-291. doi: 10.4236/apm.2013.32040.

N. Youssef and A. Soleiman, "Concircular π-Vector Fields and Special Finsler Spaces,"

References

[1] K. Yano, “Sur le Prarallélisme et la Concourance Dans l’Espaces de Riemann,” Proceedings of the Imperial Academy of Japan, Vol. 19, No. 4, 1943, pp. 189-197. doi:10.3792/pia/1195573583

[2] S. Tachibana, “On Finsler Spaces which Admit a Concurrent Vector Field,” Tensor, N. S., Vol. 1, 1950, pp. 1-5.

[3] M. Matsumoto and K. Eguchi, “Finsler Spaces Admitting a Concurrent Vector Field,” Tensor, N. S., Vol. 28, 1974, pp. 239-249.

[4] N. L. Youssef, S. H. Abed and A. Soleiman, “Concurrent π-Vector Fields and Eneregy β-Change,” International Journal of Geometric Methods in Modern Physics, Vol. 6, No. 6, 2009, pp. 1003-1031. doi:10.1142/S0219887809003904

[5] T. Adat and T. Miyazawa, “On Riemannian Spaces which Admit a Concircular Vector Field,” Tensor, N. S., Vol. 18, No. 3, 1967, pp. 335-341.

[6] B. N. Prasad, V. P. Singh and Y. P. Singh, “On Concircular Vector Fields in Finsler Spaces,” Indian Journal of Pure and Applied Mathematics, Vol. 17, No. 8, 1986, pp. 998-1007.

[7] N. L. Youssef, S. H. Abed and A. Soleiman, “A Global Approach to the Theory of Special Finsler Manifolds,” Kyoto Journal of Mathematics, Vol. 48, No. 4, 2008, pp. 857-893.

[8] N. L. Youssef, S. H. Abed and A. Soleiman, “A Global Approach to the Theory of Connections in Finsler Geometry,” Tensor, N. S., Vol. 71, No. 3, 2009, pp. 187-208.

[9] N. L. Youssef, S. H. Abed and A. Soleiman, “Cartan and Berwald Connections in the Pullback Formalism,” Algebras, Groups and Geometries, Vol. 25, No. 4, 2008, pp. 363-386.

[10] N. L. Youssef, S. H. Abed and A. Soleiman, “Geometric Objects Associated with the Fundumental Connections in Finsler Geometry,” Journal of the Egyptian Mathematical Society, Vol. 18, No. 1, 2010, pp. 67-90.

[11] F. Brickell, “A New Proof of Deicke’s Theorem on Homogeneous Functions,” Proceedings of the American Mathematical Society, Vol. 16, No. 2, 1965, pp. 190-191.

[1] K. Yano, “Sur le Prarallélisme et la Concourance Dans l’Espaces de Riemann,” Proceedings of the Imperial Academy of Japan, Vol. 19, No. 4, 1943, pp. 189-197. doi:10.3792/pia/1195573583

[2] S. Tachibana, “On Finsler Spaces which Admit a Concurrent Vector Field,” Tensor, N. S., Vol. 1, 1950, pp. 1-5.

[3] M. Matsumoto and K. Eguchi, “Finsler Spaces Admitting a Concurrent Vector Field,” Tensor, N. S., Vol. 28, 1974, pp. 239-249.

[4] N. L. Youssef, S. H. Abed and A. Soleiman, “Concurrent π-Vector Fields and Eneregy β-Change,” International Journal of Geometric Methods in Modern Physics, Vol. 6, No. 6, 2009, pp. 1003-1031. doi:10.1142/S0219887809003904

[5] T. Adat and T. Miyazawa, “On Riemannian Spaces which Admit a Concircular Vector Field,” Tensor, N. S., Vol. 18, No. 3, 1967, pp. 335-341.

[6] B. N. Prasad, V. P. Singh and Y. P. Singh, “On Concircular Vector Fields in Finsler Spaces,” Indian Journal of Pure and Applied Mathematics, Vol. 17, No. 8, 1986, pp. 998-1007.

[7] N. L. Youssef, S. H. Abed and A. Soleiman, “A Global Approach to the Theory of Special Finsler Manifolds,” Kyoto Journal of Mathematics, Vol. 48, No. 4, 2008, pp. 857-893.

[8] N. L. Youssef, S. H. Abed and A. Soleiman, “A Global Approach to the Theory of Connections in Finsler Geometry,” Tensor, N. S., Vol. 71, No. 3, 2009, pp. 187-208.

[9] N. L. Youssef, S. H. Abed and A. Soleiman, “Cartan and Berwald Connections in the Pullback Formalism,” Algebras, Groups and Geometries, Vol. 25, No. 4, 2008, pp. 363-386.

[10] N. L. Youssef, S. H. Abed and A. Soleiman, “Geometric Objects Associated with the Fundumental Connections in Finsler Geometry,” Journal of the Egyptian Mathematical Society, Vol. 18, No. 1, 2010, pp. 67-90.

[11] F. Brickell, “A New Proof of Deicke’s Theorem on Homogeneous Functions,” Proceedings of the American Mathematical Society, Vol. 16, No. 2, 1965, pp. 190-191.