Research Article
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Year 2024, Volume: 6 Issue: 1, 9 - 20
https://doi.org/10.54286/ikjm.1378951

Abstract

References

  • A. Bejancu and H. R. Farran, On the vertical bundle of a pseudo-Finsler manifold, International Journal of Mathematics and Mathematical Sciences, 22(3), (1999) 637-642.
  • A. Bejancu and H. R. Farran, Geometry of pseudo-Finsler submanifolds. Vol. 527, Springer Science and Business Medi, (2013).
  • A. F. Sağlamer, N. Kılıç and N. Çalışkan, Kenmotsu Pseudo-Metric Finsler Structures, Bulletin of Mathematical Analysis and Applications, 11(2), (2019) 12-31.
  • B. B Sinha and R. K. Yadav, 1988. On almost contact Finsler structures on vector bundle, Indian Journal of Pure and Applied Mathematics, 19(1), (1988) 27-35.
  • G. S. Asanov, Finsler Geometry, Relativity and Gauge Theories, Reidel Publication Com. Dordrecht, (1985).
  • J. A. Oubiña, New Class of almost contact metric structure, Publicationes Mathematicae Debrecen, 32, (1985) 187-193.
  • J. K. Beem, Indefinite Finsler spaces and timelike spaces, Canadian Journal of Mathematics, 22(5), (1970) 1035-1039.
  • J. K. Beem and S. S. Chern, Motions in two dimensional indefnite Finsler spaces, Indiana University Mathematics Journal, 21(6), (1971) 551-555.
  • J. K. Beem, Characterizing Finsler spaces which are pseudo-Riemannian of constant curvature, Pacific Journal of Mathematics, 64(1), (1976) 67-77. J. Szilasi, and C. Vincze, A new look at Finsler connections and special Finsler manifolds, Acta Mathematica Academıae Paedagogıcae, 16, (2000) 33-36.
  • K. Kenmotsu, A class of almost contact Riemannian manifolds. Tokohu Mathematical Journal, 24, (1972) 93-103.
  • M. D. Siddiqi, A. N. Siddiqui and O. Bahadır, Generalized Wintgen inequalities for submanifolds of trans-Sasakian space form, Journal of the Mathematical Society of the Philippines, ISSN 0115-6926 (2021) Vol. 44 No. 1 pp. 1-14.
  • M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces. Kaiseisha Press, (1986).
  • P.L. Antonelli, Handbook of Finsler geometry, Vol.2, Springer Science and Business Media, (2003).
  • R. Miron, On Finsler Spaces, Proc. Nat. Semi. 2-Brasov, (1982) 147-188.
  • R. Prasad, U. K. Gautam, J. Prakash and A. K. Rai, On (\varepsilon)−Lorentzian trans-Sasakian manifolds, GANITA, Vol. 69(2), (2019) 15-30.

Trans-Sasakian Manifolds with Pseudo Finsler Metric

Year 2024, Volume: 6 Issue: 1, 9 - 20
https://doi.org/10.54286/ikjm.1378951

Abstract

We introduce some properties and results for trans-Sasakian structures on indefinite Finsler manifolds in this paper. These structures are established on the 〖(M^0)〗^h and 〖(M^0)〗^v vector subbundles where M is an (2n+1) dimensional C^∞ manifold, M^0 is a non-empty open submanifold of TM. F^* is the fundamental Finsler function and〖 F〗^(2n+1)= (M,M^0,F^*) is an indefinite Finsler manifold. Furthermore, we give some formulas for α-Sasakian and β-Kenmotsu Finsler manifolds with pseudo-Finsler metric.

References

  • A. Bejancu and H. R. Farran, On the vertical bundle of a pseudo-Finsler manifold, International Journal of Mathematics and Mathematical Sciences, 22(3), (1999) 637-642.
  • A. Bejancu and H. R. Farran, Geometry of pseudo-Finsler submanifolds. Vol. 527, Springer Science and Business Medi, (2013).
  • A. F. Sağlamer, N. Kılıç and N. Çalışkan, Kenmotsu Pseudo-Metric Finsler Structures, Bulletin of Mathematical Analysis and Applications, 11(2), (2019) 12-31.
  • B. B Sinha and R. K. Yadav, 1988. On almost contact Finsler structures on vector bundle, Indian Journal of Pure and Applied Mathematics, 19(1), (1988) 27-35.
  • G. S. Asanov, Finsler Geometry, Relativity and Gauge Theories, Reidel Publication Com. Dordrecht, (1985).
  • J. A. Oubiña, New Class of almost contact metric structure, Publicationes Mathematicae Debrecen, 32, (1985) 187-193.
  • J. K. Beem, Indefinite Finsler spaces and timelike spaces, Canadian Journal of Mathematics, 22(5), (1970) 1035-1039.
  • J. K. Beem and S. S. Chern, Motions in two dimensional indefnite Finsler spaces, Indiana University Mathematics Journal, 21(6), (1971) 551-555.
  • J. K. Beem, Characterizing Finsler spaces which are pseudo-Riemannian of constant curvature, Pacific Journal of Mathematics, 64(1), (1976) 67-77. J. Szilasi, and C. Vincze, A new look at Finsler connections and special Finsler manifolds, Acta Mathematica Academıae Paedagogıcae, 16, (2000) 33-36.
  • K. Kenmotsu, A class of almost contact Riemannian manifolds. Tokohu Mathematical Journal, 24, (1972) 93-103.
  • M. D. Siddiqi, A. N. Siddiqui and O. Bahadır, Generalized Wintgen inequalities for submanifolds of trans-Sasakian space form, Journal of the Mathematical Society of the Philippines, ISSN 0115-6926 (2021) Vol. 44 No. 1 pp. 1-14.
  • M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces. Kaiseisha Press, (1986).
  • P.L. Antonelli, Handbook of Finsler geometry, Vol.2, Springer Science and Business Media, (2003).
  • R. Miron, On Finsler Spaces, Proc. Nat. Semi. 2-Brasov, (1982) 147-188.
  • R. Prasad, U. K. Gautam, J. Prakash and A. K. Rai, On (\varepsilon)−Lorentzian trans-Sasakian manifolds, GANITA, Vol. 69(2), (2019) 15-30.
There are 15 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Articles
Authors

Ayşe Funda Sağlamer

Hilal Fidan

Early Pub Date April 28, 2024
Publication Date
Submission Date October 26, 2023
Acceptance Date February 19, 2024
Published in Issue Year 2024 Volume: 6 Issue: 1

Cite

APA Sağlamer, A. F., & Fidan, H. (2024). Trans-Sasakian Manifolds with Pseudo Finsler Metric. Ikonion Journal of Mathematics, 6(1), 9-20. https://doi.org/10.54286/ikjm.1378951
AMA Sağlamer AF, Fidan H. Trans-Sasakian Manifolds with Pseudo Finsler Metric. ikjm. April 2024;6(1):9-20. doi:10.54286/ikjm.1378951
Chicago Sağlamer, Ayşe Funda, and Hilal Fidan. “Trans-Sasakian Manifolds With Pseudo Finsler Metric”. Ikonion Journal of Mathematics 6, no. 1 (April 2024): 9-20. https://doi.org/10.54286/ikjm.1378951.
EndNote Sağlamer AF, Fidan H (April 1, 2024) Trans-Sasakian Manifolds with Pseudo Finsler Metric. Ikonion Journal of Mathematics 6 1 9–20.
IEEE A. F. Sağlamer and H. Fidan, “Trans-Sasakian Manifolds with Pseudo Finsler Metric”, ikjm, vol. 6, no. 1, pp. 9–20, 2024, doi: 10.54286/ikjm.1378951.
ISNAD Sağlamer, Ayşe Funda - Fidan, Hilal. “Trans-Sasakian Manifolds With Pseudo Finsler Metric”. Ikonion Journal of Mathematics 6/1 (April 2024), 9-20. https://doi.org/10.54286/ikjm.1378951.
JAMA Sağlamer AF, Fidan H. Trans-Sasakian Manifolds with Pseudo Finsler Metric. ikjm. 2024;6:9–20.
MLA Sağlamer, Ayşe Funda and Hilal Fidan. “Trans-Sasakian Manifolds With Pseudo Finsler Metric”. Ikonion Journal of Mathematics, vol. 6, no. 1, 2024, pp. 9-20, doi:10.54286/ikjm.1378951.
Vancouver Sağlamer AF, Fidan H. Trans-Sasakian Manifolds with Pseudo Finsler Metric. ikjm. 2024;6(1):9-20.