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

Yıl 2022, , 207 - 218, 30.12.2022

Selahattin Beyendi

https://doi.org/10.30931/jetas.1185721

Öz

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.

Anahtar Kelimeler

Ricci soliton, α-cosymplectic manifold, non-symmetric non-metric connection, semi-symmetric, Ricci semi-symmetric

Kaynakça

• [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.