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Some Results on α-cosymplectic Manifolds Admitting a Non-symmetric Non-metric Connection

Year 2022, Volume: 7 Issue: 3, 207 - 218, 30.12.2022
https://doi.org/10.30931/jetas.1185721

Abstract

In this study, we study α-cosymplectic manifolds admitting a non-symmetric non-metric connection. Moreover, several results about Ricci semi-symmetric and semi-symmetric α-cosymplectic manifolds admitting the non-symmetric non-metric connection are going to be obtained.

References

  • [1] Ageshe, N. S. and Chafle, M. R., "A semi-symmetric non-metric connection on a Riemannian manifold", Indian J. Pure Appl. Math., 23 (1992) : 339-409.
  • [2] Aktan, N., Yıldırım, M., Murathan, C., "Almost f-cosymplectic manifolds", Mediterr J. Math., 11(2) (2014) : 775-787.
  • [3] Bagewadi, C. S. and Ingalahalli, G., "Ricci solitons in Lorentzian α-Sasakian manifolds", Acta Math. Acad. P. N., Vol-28 (2012) : 59-68.
  • [4] Barman, A. and De, U. C., "Semi-symmetric non-metric connections on Kenmotsu manifolds", Romanian J. Math. Comp. Sci., 5 (2014) : 13-24.
  • [5] Beyendi, S., Ayar, G., Aktan, N, "On a type of α-cosymplectic manifolds, Commun", Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (2019) : 852-861.
  • [6] Beyendi, S., Yıldırım, M., "On generalized weakly symmetric α-cosymplectic manifolds", Hacet. J. Math. Stat, Vol: 50 (6) (2021) : 1745-1755.
  • [7] Blair, D. E., "Contact manifolds in Riemannian geometry", Lecture Notes in Math. 509, Springer-Verlag, Berlin, (1976).
  • [8] Chaubey, S. K., "On semi-symmetric non-metric connection", Prog. of Math., 41-42 (2007) : 11-20.
  • [9] Chaubey, S. K., "Almost contact metric manifolds admitting semisymmetric non-metric connection", Bulletin of Mathematical Analysis and Applications, 3(2) (2011) : 552-560.
  • [10] Chaubey, S. K. and Ojha, R. H., "On a semi-symmetric non-metric connection", Filomat, Vol-26:2 (2012) : 63-69.
  • [11] Chaubey, S. K. and Pandey, A. C., "Some properties of a semisymmetric Non-metric connection on a Sasakian manifold", Int. J. Contemp. Math. Science, Vol-8, No. 16 (2013) : 789-799.
  • [12] De, U. C. and Biswas, S. C., "On a type of semi-symmetric non-metric connection on a Riemannian manifold", Ganita, 48 (1997) : 91-94.
  • [13] Erken, I. K., "On a classification of almost α-cosymplectic manifolds", Khayyam J. Math., 5 (2019) : 1-10.
  • [14] Friedmann, A. and Schouten, J. A., "Uber die geometrie der halbsymmetrischen ubertragung", Math. Zeitschr. 21 (1924) : 211-223.
  • [15] Goldberg, S. I. and Yano, K., "Integrability of almost cosymplectic structure", Pac. J. Math., 31 (1969) : 373-381.
  • [16] Hayden, H. A., "Subspace of a space with torsion", Proc. London Math. Soc., 34 (1932) : 27– 50.
  • [17] Haseeb, A., "On concircular curvature tensor with respect to the semi-symmetric non-metric connection in a Kenmotsu manifold", Kyungpook Math. J., 56 (2016) : 951-964.
  • [18] Kenmotsu, K., "A class of almost contact Riemannian manifolds", Tohoku Math. J., 24(1) (1972) : 93-103.
  • [19] Kim, T. W., Pak, H. K., "Canonical foliations of certain classes of almost contact metric structures", Acta Math, Sinica, Eng. Ser. Aug., 21(4) (2005) : 841-846.
  • [20] Lie, S., "Geometrie der Berührungstransformationen", B.G. Teubner, Leipzig, (1896).
  • [21] Olszak, Z., "On almost cosymplectic manifolds", Kodai Math., 4 (2) (1981) : 239- 250.
  • [22] Öztürk, H., Murathan, C., Aktan, N., Vanli, A. T., "Almost α-cosymplectic f-manifolds", An. Stiint. Univ. Al. I. Cuza Iasi Mat., (N.S.) 60(1) (2014) : 211–226.
  • [23] Pankaj, Chaubey, S. K. and Prasad, R., "Trans-Sasakian manifolds with respect to a non-symmetric nonmetric connection", Global Journal of Advanced Research on Classical and Modern Geometries, Vol.7 (2018) : Issue 1, 1-10.
  • [24] Pankaj, Chaubey, S. K. and Prasad, R., "Sasakian manifolds admitting a non-symmetric non-metric connection", Palestina journal of mathematic, Vol. 9(2) (2020) : 698-710.
  • [25] Prasad, R. and Pankaj, "Some curvature tensors on a trans-Sasakian manifold with respect to semisymmetric non-metric connection", J.Nat. Acad. Math, Sp. Volume (2009) : 55-64.
  • [26] Schouten, J. A., "Ricci-calculus", Springer-Verlag. Berlin, 1954.
  • [27] Singh, A., Mishra, C. K., Kumar, L. And Patel, S., "Characterization of Kenmotsu manifolds admitting a non-symmetric non-metric connection", J. Int. Acad. Phys. Sci., Vol. 26, No. 3 (2022) : 265-274.
  • [28] Vaisman, K., "Conformal changes of almost contact metric manifolds", In Lecture Notes in Mathematics 792, Springer, Berlin, (1980) : 435-443.
  • [29] Yano, K., "On semisymmetric metric connections", Rev. Roumaine Math. Press Apple. 15 (1970) : 1579-1586.
Year 2022, Volume: 7 Issue: 3, 207 - 218, 30.12.2022
https://doi.org/10.30931/jetas.1185721

Abstract

References

  • [1] Ageshe, N. S. and Chafle, M. R., "A semi-symmetric non-metric connection on a Riemannian manifold", Indian J. Pure Appl. Math., 23 (1992) : 339-409.
  • [2] Aktan, N., Yıldırım, M., Murathan, C., "Almost f-cosymplectic manifolds", Mediterr J. Math., 11(2) (2014) : 775-787.
  • [3] Bagewadi, C. S. and Ingalahalli, G., "Ricci solitons in Lorentzian α-Sasakian manifolds", Acta Math. Acad. P. N., Vol-28 (2012) : 59-68.
  • [4] Barman, A. and De, U. C., "Semi-symmetric non-metric connections on Kenmotsu manifolds", Romanian J. Math. Comp. Sci., 5 (2014) : 13-24.
  • [5] Beyendi, S., Ayar, G., Aktan, N, "On a type of α-cosymplectic manifolds, Commun", Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (2019) : 852-861.
  • [6] Beyendi, S., Yıldırım, M., "On generalized weakly symmetric α-cosymplectic manifolds", Hacet. J. Math. Stat, Vol: 50 (6) (2021) : 1745-1755.
  • [7] Blair, D. E., "Contact manifolds in Riemannian geometry", Lecture Notes in Math. 509, Springer-Verlag, Berlin, (1976).
  • [8] Chaubey, S. K., "On semi-symmetric non-metric connection", Prog. of Math., 41-42 (2007) : 11-20.
  • [9] Chaubey, S. K., "Almost contact metric manifolds admitting semisymmetric non-metric connection", Bulletin of Mathematical Analysis and Applications, 3(2) (2011) : 552-560.
  • [10] Chaubey, S. K. and Ojha, R. H., "On a semi-symmetric non-metric connection", Filomat, Vol-26:2 (2012) : 63-69.
  • [11] Chaubey, S. K. and Pandey, A. C., "Some properties of a semisymmetric Non-metric connection on a Sasakian manifold", Int. J. Contemp. Math. Science, Vol-8, No. 16 (2013) : 789-799.
  • [12] De, U. C. and Biswas, S. C., "On a type of semi-symmetric non-metric connection on a Riemannian manifold", Ganita, 48 (1997) : 91-94.
  • [13] Erken, I. K., "On a classification of almost α-cosymplectic manifolds", Khayyam J. Math., 5 (2019) : 1-10.
  • [14] Friedmann, A. and Schouten, J. A., "Uber die geometrie der halbsymmetrischen ubertragung", Math. Zeitschr. 21 (1924) : 211-223.
  • [15] Goldberg, S. I. and Yano, K., "Integrability of almost cosymplectic structure", Pac. J. Math., 31 (1969) : 373-381.
  • [16] Hayden, H. A., "Subspace of a space with torsion", Proc. London Math. Soc., 34 (1932) : 27– 50.
  • [17] Haseeb, A., "On concircular curvature tensor with respect to the semi-symmetric non-metric connection in a Kenmotsu manifold", Kyungpook Math. J., 56 (2016) : 951-964.
  • [18] Kenmotsu, K., "A class of almost contact Riemannian manifolds", Tohoku Math. J., 24(1) (1972) : 93-103.
  • [19] Kim, T. W., Pak, H. K., "Canonical foliations of certain classes of almost contact metric structures", Acta Math, Sinica, Eng. Ser. Aug., 21(4) (2005) : 841-846.
  • [20] Lie, S., "Geometrie der Berührungstransformationen", B.G. Teubner, Leipzig, (1896).
  • [21] Olszak, Z., "On almost cosymplectic manifolds", Kodai Math., 4 (2) (1981) : 239- 250.
  • [22] Öztürk, H., Murathan, C., Aktan, N., Vanli, A. T., "Almost α-cosymplectic f-manifolds", An. Stiint. Univ. Al. I. Cuza Iasi Mat., (N.S.) 60(1) (2014) : 211–226.
  • [23] Pankaj, Chaubey, S. K. and Prasad, R., "Trans-Sasakian manifolds with respect to a non-symmetric nonmetric connection", Global Journal of Advanced Research on Classical and Modern Geometries, Vol.7 (2018) : Issue 1, 1-10.
  • [24] Pankaj, Chaubey, S. K. and Prasad, R., "Sasakian manifolds admitting a non-symmetric non-metric connection", Palestina journal of mathematic, Vol. 9(2) (2020) : 698-710.
  • [25] Prasad, R. and Pankaj, "Some curvature tensors on a trans-Sasakian manifold with respect to semisymmetric non-metric connection", J.Nat. Acad. Math, Sp. Volume (2009) : 55-64.
  • [26] Schouten, J. A., "Ricci-calculus", Springer-Verlag. Berlin, 1954.
  • [27] Singh, A., Mishra, C. K., Kumar, L. And Patel, S., "Characterization of Kenmotsu manifolds admitting a non-symmetric non-metric connection", J. Int. Acad. Phys. Sci., Vol. 26, No. 3 (2022) : 265-274.
  • [28] Vaisman, K., "Conformal changes of almost contact metric manifolds", In Lecture Notes in Mathematics 792, Springer, Berlin, (1980) : 435-443.
  • [29] Yano, K., "On semisymmetric metric connections", Rev. Roumaine Math. Press Apple. 15 (1970) : 1579-1586.
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Selahattin Beyendi 0000-0002-1037-6410

Early Pub Date December 30, 2022
Publication Date December 30, 2022
Published in Issue Year 2022 Volume: 7 Issue: 3

Cite

APA Beyendi, S. (2022). Some Results on α-cosymplectic Manifolds Admitting a Non-symmetric Non-metric Connection. Journal of Engineering Technology and Applied Sciences, 7(3), 207-218. https://doi.org/10.30931/jetas.1185721
AMA Beyendi S. Some Results on α-cosymplectic Manifolds Admitting a Non-symmetric Non-metric Connection. JETAS. December 2022;7(3):207-218. doi:10.30931/jetas.1185721
Chicago Beyendi, Selahattin. “Some Results on α-Cosymplectic Manifolds Admitting a Non-Symmetric Non-Metric Connection”. Journal of Engineering Technology and Applied Sciences 7, no. 3 (December 2022): 207-18. https://doi.org/10.30931/jetas.1185721.
EndNote Beyendi S (December 1, 2022) Some Results on α-cosymplectic Manifolds Admitting a Non-symmetric Non-metric Connection. Journal of Engineering Technology and Applied Sciences 7 3 207–218.
IEEE S. Beyendi, “Some Results on α-cosymplectic Manifolds Admitting a Non-symmetric Non-metric Connection”, JETAS, vol. 7, no. 3, pp. 207–218, 2022, doi: 10.30931/jetas.1185721.
ISNAD Beyendi, Selahattin. “Some Results on α-Cosymplectic Manifolds Admitting a Non-Symmetric Non-Metric Connection”. Journal of Engineering Technology and Applied Sciences 7/3 (December 2022), 207-218. https://doi.org/10.30931/jetas.1185721.
JAMA Beyendi S. Some Results on α-cosymplectic Manifolds Admitting a Non-symmetric Non-metric Connection. JETAS. 2022;7:207–218.
MLA Beyendi, Selahattin. “Some Results on α-Cosymplectic Manifolds Admitting a Non-Symmetric Non-Metric Connection”. Journal of Engineering Technology and Applied Sciences, vol. 7, no. 3, 2022, pp. 207-18, doi:10.30931/jetas.1185721.
Vancouver Beyendi S. Some Results on α-cosymplectic Manifolds Admitting a Non-symmetric Non-metric Connection. JETAS. 2022;7(3):207-18.