Some more results on an epsilon-Kenmotsu manifold with a semi-symmetric semi-metric connection
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Abstract
The objective of the present paper is to study some new results on an epsilon-Kenmotsu manifold with a semi-symmetric metric connection. It is shown that the manifold satisfying the conditions $\bar{R}. \bar{S} = 0$ and $\bar{S}. \bar{R} = 0$ is an η-Einstein manifold. Also, we obtain the conditions for the manifold with a semi-symmetric metric connection to be conformally flat.
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Haseeb, A., Khan, M., & Siddiqi, M.
(2016).
Some more results on an epsilon-Kenmotsu manifold with a semi-symmetric semi-metric connection.
Acta Mathematica Universitatis Comenianae, 85(1), 9-20.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/97/275
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References
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[15] Yano, K. and Kon, M., Structures onManifolds, Series in Pure Math., Vol. 3, World Sci., 1984.
[2] Bartolotti, E., Sulla geometria della variata a onnection affine. Ann. di Mat. 4(8) (1930), 53-101.
[3] Bejancu A. and Duggal K. L., Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math. Math. Sci. 16(1993), no. 3, 545-556.
[4] Blair, D. E., Contact manifolds in Riemannian geometry, Lecture note in Mathematics, 509, Springer-Verlag Berlin-New York, 1976.
[5] De, U. C. and Sarkar, A., On ǫ-Kenmotsu manifold, Hardonic J. 32 (2009), no.2, 231-242.
[6] Friedmann, A. and Schouten, J. A., Uber die Geometric der halbsymmetrischen Ubertragung, Math. Z. 21 (1924), 211-223.
[7] Hayden, H. A., Subspaces of space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.
[8] Jun, J. B., De, U. C. and Pathak, G., On Kenmotsu manifolds, J. Korean Math. Soc. 42 (2005), no. 3, 435-445.
[9] Kenmotsu, K., A class of almost contact Riemannian manifold, Tohoku Math. J., 24 (1972), 93-103.
[10] Pathak, G. and De, U. C., On a semi-symmetric connection in a Kenmotsu manifold, Bull. Calcutta Math. Soc. 94 (2002), no. 4, 319-324.
[11] Tripathi, M. M., On a semi-symmetric metric connection in a Kenmotsu manifold, J. Pure Math. 16(1999), 67-71.
[12] Tripathi, M. M., Kilic, E., Perktas S. Y. and Keles, S., Indefinite almost para-contact metric manifolds, Int. J. Math. and Math. Sci. (2010), art. id 846195, pp. 19.
[13] Xufeng, X. and Xiaoli, C., Two theorem on ǫ-Sasakian manifolds, Int. J. Math. Math. Sci. 21 (1998), no. 2, 249-54.
[14] Yano, K., On semi-symmetric metric connections, Revue Roumaina De Math. Pures Appl. 15(1970), 1579-1586.
[15] Yano, K. and Kon, M., Structures onManifolds, Series in Pure Math., Vol. 3, World Sci., 1984.