Projective Curvature Tensor on N($\kappa$)-Contact Metric Manifold Admitting Semi-Symmetric Non-Metric Connection

Year 2020, Volume: 3 Issue: 2, 94 - 100, 15.12.2020

Mustafa Altın

https://doi.org/10.33401/fujma.733415

Cited By: 2

Abstract

The object of the present paper is to classify $N(\kappa)$-contact metric manifolds admitting the semi-symmetric non-metric connection with certain curvature conditions the projectively curvature tensor. We studied projective flat, $\xi- $projectively flat, $\phi- $projectively flat $N(\kappa )$-contact metric manifolds admitting the semi-symmetric non-metric connection. Also, we examine such manifolds under some local symmetry conditions related to projective curvature tensor.

Keywords

$N(\kappa)$-contact metric manifolds, Projective curvature tensor, Semi-symmetric non-metric connection

References

• [1] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics 203, Boston, MA: Birkhauser Boston, Inc., 2002.
• [2] D. E. Blair, T. Koufogiorgos, B.J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91 (1995), 189-214.
• [3] S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Math. J., 40 (1988), 441-448.
• [4] D. E. Blair, Two remarks on contact metric structures, Tohoku Math. J., 29 (1977), 319-324.
• [5] S. Ghosh, U. C. De, A. Taleshian, Conharmonic curvature tensor on N(k)-contact metric manifolds, ISRN Geometry, (2011), Art. ID 423798, 11 pages.
• [6] A. Kazan, S. Kazan Sasakian statistical manifolds with semi-symmetric metric Connection, Univers. J. Math. Appl., 1(4) (2018), 226-232.
• [7] M. Y. Yılmaz, M. Bektas¸, Curvature inequalities between a Hessian manifold with constant curvature and its submanifolds, Math. Sci. Appl. E-Notes, 5 (1) (2017), 27-33.
• [8] U. C. De, A. K. Gazi, On f-recurrent N(k)-contact metric manifolds, Math. J. Okayama Univ., 50 (2008), 101-112.
• [9] C. Özgur, S. Sular, On N(k)-contact metric manifolds satisfying certain conditions, Sut. J. Math., 44 (2008), 89-99.
• [10] N. S. Agashe, M. R. Chafle, A semi-symmetric non-metric connection on a Riemannian Manifold, Indian J. Pure Appl. Math., 23(6) (1992), 399-409.
• [11] A. Vanlı Turgut, İ. Ünal, D. Özdemir, Normal complex contact metric manifolds admitting a semi symmetric metric connection, Applied Mathematics and Nonlinear Sciences 5(2) (2020), 49-66.
• [12] A. Barman, Semi-symmetric non-metric connection in a P-Sasakian manifold, Novi Sad J. Math., 43 (2013), 117-124.
• [13] A. Barman, U. C. De, Semi-symmetric non-metric connections on Kenmotsu manifolds, Romanian J. Math. and Comp. Sci., 5 (2014), 13-24.
• [14] U. C. De, S. C. Biswas, On a type of semi-symmetric non-metric connection on a Riemannian manifold, Ganita, 48 (1997), 91-94.
• [15] O. C. Andonie, On semi-symmetric non-metric connection on a Riemannian manifold, Ann. Fac. Sci. De Kinshasa, Zaire Sect. Math. Phys., 2 (1976).
• [16] P. Majhi, U. C. De, Classifications on N(k)-contact metric manifolds satisfying certain curvature conditions, Acta Math. Univ. Comenianae, 84 (2015), 167-178.
• [17] G.Ayar, S. K.Chaubey, M-projective curvature tensor over cosymplectic manifolds, Differential Geometry-Dynamical Systems, 21 (2019), 23-33.
• [18] G. Ayar, P. Tekin, N. Aktan, Some Curvature Conditions on Nearly Cosymplectic Manifolds, Indian J. Industrial Appl. Math., 10 (2019), 51-60.
• [19] G. Ayar and D. Demirhan, Ricci Solitons on Nearly Kenmotsu Manifolds with Semi symmetric Metric Connection, J. Eng. Tech. Appl. Sci., 4(3) (2019), 131–140.
• [20] A. Turgut Vanli, İ. Ünal, Conformal, concircular, quasi-conformal and conharmonic flatness on normal complex contact metric manifolds, Int. J. Geom. Methods Mod. Phys., 14(05) (2017), 1750067.
• [21] İ. Ünal, R. Sarı, A. Vanlı Turgut, Concircular curvature tensor on generalized kenmotsu manifolds, Gu¨mu¨s¸hane U¨ niversitesi Fen Bilimleri Enstitüsü Dergisi, (2018), 99-105.
• [22] A.Turgut Vanli, İ. Ünal, H-curvature tensors on IK-normal complex contact metric manifolds, International Journal of Geometric Methods in Modern Physics, 15(12) (2018) 1850205.
• [23] A. Yıldız, U. C. De, M. Cengizhan, K. Arslan, On the Weyl projective curvature tensor of an N(k) -contact metric manifold, Mathematica Pannonica, 21(1) (2010), 1-14.
• [24] A. Barman, On N(k)-contact metric manifolds admitting a type of a semi-symmetric non-metric connection, Acta Math. Univ. Comenianae, LXXXVI 1 (2017), 81-90.
• [25] E. Boeckx, A full classification of concat metric (k;m)-spaces, Illinois J. Math., 44 (2000), 212-219.
• [26] D. E.Blair, J. S. Kim, M. M. Tripathi, On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc., 42 (2005), 883-892.