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Year 2023, Volume: 52 Issue: 1, 136 - 150, 15.02.2023
https://doi.org/10.15672/hujms.1081955

Abstract

References

  • [1] N. S. Agashe and M. R. Chafle, A semi-symmetric non-metric connection in a Riemannian manifolds, Indian J. Pure Appl. Math. 23, 399-409, 1992.
  • [2] O. C. Andonie and D. Smaranda, Certaines connexions semi-symètriques, Tensor, N. S. 31, 8-12, 1977.
  • [3] G. B. Folland, Weyl manifolds, J. Diff. Geom. 4, 143-153, 1970.
  • [4] J. Grifone, Structure présque-tangente et connexions, I, Ann. Inst. Fourier, Grenoble, 22 (1), 287-334, 1972.
  • [5] J. Grifone, Structure presque-tangente et connexions, II, Ann. Inst. Fourier, Grenoble, 22 (3), 291-338, 1972.
  • [6] H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34, 27-50, 1932.
  • [7] J. Klein and A. Voutier, Formes extérieures génératrices de sprays, Ann. Inst. Fourier, Grenoble, 18 (1), 241-260, 1968.
  • [8] Y. Liang, On semi-symmetric recurrent-metric connection, Tensor, N. S. 55, 107-112, 1994.
  • [9] M. Matsumoto, The theory of Finsler connections, Publication of the study group of geometry, 5, Dept. Math., Okayama Univ. 1970.
  • [10] M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha Press, Japan, 1986.
  • [11] R. Miron and M. Anastasiei, The geometry of Lagrange spaces: Theory and applications, Kluwer Acad. Publ. 1994.
  • [12] R. S. Mishra and S. N. Pandey, On quarter-symmetric metric F-connections, Tensor, N. S. 34, 1-7, 1980.
  • [13] B. N. Prasad and L. Srivastava, On hv-recurrent Finsler connection, Indian J. Pure Appl. Math. 20, 790-798, 1989.
  • [14] H. Rund, The differential geometry of Finsler spaces, Springer-Verlag, Berlin, 1959.
  • [15] J. Sengupta, U. C. De and T. Q. Binh, On a type of semi-symmetric non-metric connection on Riemannian manifolds, Indian J. Pure Appl. Math. 31, 659-1670, 2000.
  • [16] A. Soleiman, S. G. Elgendi and A. M. Abdelsalam, A new general Finsler connection, J. Finsler Geom. Appl. (JFGA), 1, 1-14, 2020.
  • [17] J. Szilasi, R. L. Lovas and D. Cs Kertesz, Connections, Sprays and Finsler structures, World Scientific, 2014.
  • [18] W. Tang, T. Ho, K. Ri, F. Fu and P. Zhao, On a generalized quarter symmetric metric recurrent connection, Filomat 32 (1) , 207-215, 2018.
  • [19] M. M. Tripathi, A new connection in a Riemannian manifold, Int. Electronic J. Geom. 1, 15-24, 2008.
  • [20] Cs. Vincze, On a special type of generalized Berwald manifolds: semi-symmetric linear connections preserving theFinslerian length of tangent vectors, European J. Math. 3, 1098-1171, 2017.
  • [21] K. Yano, On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15, 1579-1586, 1970.
  • [22] K. Yano, Integral formulas in Riemannian geometry, Marcel Dekker Inc. 1970.
  • [23] K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors, Tensor, N. S. 38, 13-18, 1984.
  • [24] Nabil L. Youssef, Connexions métiques semi-symétriques semi-basiques, Tensor, N. S. 40, 242-248, 1983.
  • [25] Nabil L. Youssef, Vertical semi-symmetric metric connections Tensor, N. S., 49, 218- 229, 1990.
  • [26] Nabil L. Youssef and A. Soleiman, On horizontal recurrent Finsler connection, Rend. Circ. Mat. Palermo, II. Ser, 68, 1-9, 2019.
  • [27] Nabil L. Youssef, S. H. Abed and A. Soleiman, Cartan and Berwald connections in the pullback formalism, Algebras, Groups and Geometries, 25, 363-384, 2008.
  • [28] Nabil L. Youssef, S. H. Abed and A. Soleiman, A global approach to the theory of special Finsler manifolds, J. Math. Kyoto Univ. 48, 857-893, 2008.
  • [29] Nabil L. Youssef, S. H. Abed and A. Soleiman, A global approach to the theory of connections in Finsler geometry, Tensor, N. S. 71, 187-208, 2009.
  • [30] Nabil L. Youssef, S. H. Abed and A. Soleiman, Geometric objects associated with the fundamental connections in Finsler geometry, J. Egypt. Math. Soc. 18, 67-90, 2010.

Tripathi connection in Finsler geometry

Year 2023, Volume: 52 Issue: 1, 136 - 150, 15.02.2023
https://doi.org/10.15672/hujms.1081955

Abstract

Adopting the pullback formalism, a new linear connection in Finsler geometry has been introduced and investigated. Such connection unifies all formerly known Finsler connections and some other connections not introduced so far. Also, our connection is a Finslerian version of the Tripathi connection introduced in Riemannian geometry. The existence and uniqueness of such connection is proved intrinsically. An explicit intrinsic expression relating this connection to Cartan connection is obtained. Some generalized Finsler connections are constructed from Tripathi Finsler connection, by applying the ${P}^{1}$-process and ${C}$-process introduced by Matsumoto. Finally, under certain conditions, many special Finsler connections are given.

References

  • [1] N. S. Agashe and M. R. Chafle, A semi-symmetric non-metric connection in a Riemannian manifolds, Indian J. Pure Appl. Math. 23, 399-409, 1992.
  • [2] O. C. Andonie and D. Smaranda, Certaines connexions semi-symètriques, Tensor, N. S. 31, 8-12, 1977.
  • [3] G. B. Folland, Weyl manifolds, J. Diff. Geom. 4, 143-153, 1970.
  • [4] J. Grifone, Structure présque-tangente et connexions, I, Ann. Inst. Fourier, Grenoble, 22 (1), 287-334, 1972.
  • [5] J. Grifone, Structure presque-tangente et connexions, II, Ann. Inst. Fourier, Grenoble, 22 (3), 291-338, 1972.
  • [6] H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34, 27-50, 1932.
  • [7] J. Klein and A. Voutier, Formes extérieures génératrices de sprays, Ann. Inst. Fourier, Grenoble, 18 (1), 241-260, 1968.
  • [8] Y. Liang, On semi-symmetric recurrent-metric connection, Tensor, N. S. 55, 107-112, 1994.
  • [9] M. Matsumoto, The theory of Finsler connections, Publication of the study group of geometry, 5, Dept. Math., Okayama Univ. 1970.
  • [10] M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha Press, Japan, 1986.
  • [11] R. Miron and M. Anastasiei, The geometry of Lagrange spaces: Theory and applications, Kluwer Acad. Publ. 1994.
  • [12] R. S. Mishra and S. N. Pandey, On quarter-symmetric metric F-connections, Tensor, N. S. 34, 1-7, 1980.
  • [13] B. N. Prasad and L. Srivastava, On hv-recurrent Finsler connection, Indian J. Pure Appl. Math. 20, 790-798, 1989.
  • [14] H. Rund, The differential geometry of Finsler spaces, Springer-Verlag, Berlin, 1959.
  • [15] J. Sengupta, U. C. De and T. Q. Binh, On a type of semi-symmetric non-metric connection on Riemannian manifolds, Indian J. Pure Appl. Math. 31, 659-1670, 2000.
  • [16] A. Soleiman, S. G. Elgendi and A. M. Abdelsalam, A new general Finsler connection, J. Finsler Geom. Appl. (JFGA), 1, 1-14, 2020.
  • [17] J. Szilasi, R. L. Lovas and D. Cs Kertesz, Connections, Sprays and Finsler structures, World Scientific, 2014.
  • [18] W. Tang, T. Ho, K. Ri, F. Fu and P. Zhao, On a generalized quarter symmetric metric recurrent connection, Filomat 32 (1) , 207-215, 2018.
  • [19] M. M. Tripathi, A new connection in a Riemannian manifold, Int. Electronic J. Geom. 1, 15-24, 2008.
  • [20] Cs. Vincze, On a special type of generalized Berwald manifolds: semi-symmetric linear connections preserving theFinslerian length of tangent vectors, European J. Math. 3, 1098-1171, 2017.
  • [21] K. Yano, On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15, 1579-1586, 1970.
  • [22] K. Yano, Integral formulas in Riemannian geometry, Marcel Dekker Inc. 1970.
  • [23] K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors, Tensor, N. S. 38, 13-18, 1984.
  • [24] Nabil L. Youssef, Connexions métiques semi-symétriques semi-basiques, Tensor, N. S. 40, 242-248, 1983.
  • [25] Nabil L. Youssef, Vertical semi-symmetric metric connections Tensor, N. S., 49, 218- 229, 1990.
  • [26] Nabil L. Youssef and A. Soleiman, On horizontal recurrent Finsler connection, Rend. Circ. Mat. Palermo, II. Ser, 68, 1-9, 2019.
  • [27] Nabil L. Youssef, S. H. Abed and A. Soleiman, Cartan and Berwald connections in the pullback formalism, Algebras, Groups and Geometries, 25, 363-384, 2008.
  • [28] Nabil L. Youssef, S. H. Abed and A. Soleiman, A global approach to the theory of special Finsler manifolds, J. Math. Kyoto Univ. 48, 857-893, 2008.
  • [29] Nabil L. Youssef, S. H. Abed and A. Soleiman, A global approach to the theory of connections in Finsler geometry, Tensor, N. S. 71, 187-208, 2009.
  • [30] Nabil L. Youssef, S. H. Abed and A. Soleiman, Geometric objects associated with the fundamental connections in Finsler geometry, J. Egypt. Math. Soc. 18, 67-90, 2010.
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Amr Soleiman This is me 0000-0002-3755-765X

Ebtsam Taha 0000-0002-3755-765X

Publication Date February 15, 2023
Published in Issue Year 2023 Volume: 52 Issue: 1

Cite

APA Soleiman, A., & Taha, E. (2023). Tripathi connection in Finsler geometry. Hacettepe Journal of Mathematics and Statistics, 52(1), 136-150. https://doi.org/10.15672/hujms.1081955
AMA Soleiman A, Taha E. Tripathi connection in Finsler geometry. Hacettepe Journal of Mathematics and Statistics. February 2023;52(1):136-150. doi:10.15672/hujms.1081955
Chicago Soleiman, Amr, and Ebtsam Taha. “Tripathi Connection in Finsler Geometry”. Hacettepe Journal of Mathematics and Statistics 52, no. 1 (February 2023): 136-50. https://doi.org/10.15672/hujms.1081955.
EndNote Soleiman A, Taha E (February 1, 2023) Tripathi connection in Finsler geometry. Hacettepe Journal of Mathematics and Statistics 52 1 136–150.
IEEE A. Soleiman and E. Taha, “Tripathi connection in Finsler geometry”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 1, pp. 136–150, 2023, doi: 10.15672/hujms.1081955.
ISNAD Soleiman, Amr - Taha, Ebtsam. “Tripathi Connection in Finsler Geometry”. Hacettepe Journal of Mathematics and Statistics 52/1 (February 2023), 136-150. https://doi.org/10.15672/hujms.1081955.
JAMA Soleiman A, Taha E. Tripathi connection in Finsler geometry. Hacettepe Journal of Mathematics and Statistics. 2023;52:136–150.
MLA Soleiman, Amr and Ebtsam Taha. “Tripathi Connection in Finsler Geometry”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 1, 2023, pp. 136-50, doi:10.15672/hujms.1081955.
Vancouver Soleiman A, Taha E. Tripathi connection in Finsler geometry. Hacettepe Journal of Mathematics and Statistics. 2023;52(1):136-50.