TARU PUBLICATIONS
Journal of Dynamical Systems and Geometric Theories cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X
Powered by:Powered by

The Journal of Dynamical Systems and Geometric Theories (JDSGT) is a world leading journal publishing high quality, rigorously peer-reviewed original research on dynamical systems and geometry, including the interactions between these two subjects and interdisciplinary research with other branches of knowledge since 2003. Topics published by the Journal include but are not limited to: Random dynamical systems Geometry and physics Dynamical systems with hyperbolic behaviour Real and complex geometry Ergodic theory Distance geometry Topological dynamics Global differential geometry Infinite-dimensional Hamiltonian systems Symplectic geometry, contact geometry The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Chief Editor’s discretion.

Issues up to 2022 co-published with and available at:Taylor & Francis
info@tarupublications.com
Open Access Research Article

On R-complex Finsler space with cubic (α,β)–metric

* , ,

* Corresponding author · click or hover a name for details

pp. 47–63Vol. 22Issue 1 & 2November 2024DOI: 10.47974/JDSGT-2024-003XML
Received:
18 Mar 2024
Published Online:
01 Nov 2024
Article type:
Research Article
Language:
EN
Article no.:
JDSGT-2024-003
Pages:
47–63

Abstract

In this paper we study about the basic geometrical properties for R-complex Finsler space which is equipped with Cubic (α,β)–metric and the metric is defined by (α + β)3/α2. We obtained the fundamental metric field g͠ij, g͠ij and the inverse of these tensor fields. Further we study the properties of non-Hermitian space for the R-complex Finsler space equipped with Cubic (α,β)-metric.

Keywords

Subject Classifications

53B4053C6053A2053B10

References

[1] B. K. Tripathi, D. Patel, and V. K. Chaubey, "Projectively flat Cubic (α, β)-Metric with constant flag curvature K = 0," Surveys in Mathematics and its Applications, vol. 19, pp. 167–178 (2024).[2] B. K. Tripathi and M. K. Singh, "On the L-Duality of a Finsler space with Special (α, β)-metric," Journal of Hyperstructures, vol. 12, no. 1, pp. 173–182 (2023).[3] B. K. Tripathi, S. Khan and M. K. Singh, “Conformally Flat Locally Minkowski Finsler Space with a Special Cubic (a, b) – Metric’’, J. Adv. Math. Stud., vol. 16, no. 3, pp. 275-281, (2023).[4] B. K. Tripathi, S. Khan, and V. K. Chaubey, "On Projectively Flat Finsler Space with a cubic (α, β)-Metric," Filomat, vol. 37, no. 26, pp. 8975–8982 (2023).[5] B. K. Tripathi and S. Khan, "On Weakly Berwald space with a special cubic (α, β)-metric," Surveys in Mathematics and its Applications, vol. 18, pp. 1–11 (2023).[6] G. Munteanu, Complex Spaces in Finsler, Lagrange and Hamilton Geometries, Kluwer Academic Publishers, vol. 141, no. 13 (2004).[7] G. Munteanu and M. Purcuru, "On R-complex Finsler spaces," Balkan Journal of Geometry and its Applications, vol. 14, pp. 15–59 (2009).[8] G. Shankar and R. K. Sharma, "R-complex Finsler space with infinite series (α, β)-metric," Bulletin of the Transilvania University of Braşov, vol. 11, no. 1 (2018).[9] G. Shankar and S. A. Baby, "R-complex Finsler spaces with special (α, β)-metric," International Journal of Applied Mathematics, vol. 29, no. 5, pp. 609–619 (2016).[10] G. Yang, "On a class of Einstein-reversible Finsler metrics," Differential Geometry and its Applications, vol. 60, pp. 80–103 (2018).[11] S. Kobayashi, "Negative vector bundles and complex Finsler metrics," Nagoya Mathematical Journal, vol. 57, pp. 153–166 (1975).[12] M. Abate and G. Patrizio, Finsler Metrics – A Global Approach, Lecture Notes in Mathematics, vol. 1591, Springer-Verlag (1994).[13] M. Matsumoto, "On theory of Finsler spaces with (α, β)-metric," Reports on Mathematical Physics, vol. 31, pp. 43–83 (1991).[14] M. Purcuru, "On R-complex Finsler spaces with Kropina metrics," Bulletin of the Transilvania University of Braşov, vol. 4(53), pp. 79–88 (2011).[15] M. Purcuru, "On R-complex Cartan space," Analele Ştiinţifice ale Universităţii "Al.I. Cuza" din Iaşi (S.N.), Matematică, vol. LIV, pp. 15–26 (2008).[16] N. Aldea and G. Munteanu, "On complex Finsler spaces with Randers metrics," Journal of the Korean Mathematical Society, vol. 46, no. 5, pp. 949–966 (2009).[17] N. Aldea and G. Munteanu, "(α, β)-Complex Finsler metrics," in Proceedings of the 4th International Colloquium 'Mathematics in Engineering and Numerical Physics', Bucharest, Romania, Oct. 6–8, pp. 1–6 (2006).[18] R. Miron, General Randers Spaces, Kluwer Academic Publishers (1996).[19] G. B. Rizza, "Strutture di Finsler di tipo quasi-Hermitian," Rivista di Matematica della Università di Parma, vol. 4, pp. 83–106 (1963).[20] T. Aikou, "Projective flatness of complex Finsler metrics," Publicationes Mathematicae Debrecen, vol. 63, pp. 343–362 (2003).[21] T. Aikou, "On Finsler geometry on complex vector bundles," in Riemann–Finsler Geometry, MSRI Publications, vol. 50, pp. 83–105 (2004).[22] V. S. Sabău and H. Shimada, "Remarkable classes of (α, β)-metric spaces," Reports on Mathematical Physics, vol. 47, no. 1, pp. 31–48 (2001).
Views: 117Downloads: 5Citations: 0