Quarter-symmetric metric connection on a Lorentzian α-Sasakian manifold

Year 2017, Volume: 5 Issue: 2, 69 - 79, 30.03.2017

Venkatesha Venkatesha , Divyashree G.

Abstract

In the present paper we study locally ϕ-symmetric, locally projective ϕ-symmetric, ϕ-recurrent and ϕ-projectively flat Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. Further, the existence of a Lorentzian α-Sasakian manifold admitting quarter-symmetric metric connection is shown by constructing an example.

Keywords

Lorentzian α-Sasakian manifold, quarter-symmetric metric connection, locally ϕ-symmetric, locally projective ϕ-symmetric, ϕ-recurrent

References

• Ajit Barman, On Lorentzian α -Sasakian manifolds admitting a type of semi-symmetric metric connection, Novi Sad J. Math., 44(2), 77-88, (2014).
• E. Bartolotti,Sulla geometria della variata a connection affine,Ann. di Mat. 4(8), 53-101, (1930).
• U. C. De and J. Sengupta, Quarter-symmetric metric connection on a Sasakian manifold,Communications de la Faculte des Sciences de l’Universite dAnkara., 49(1-2), 7-13, (2000).
• S. Dey and A. Bhattacharyya, Some properties of Lorentzian al pha-Sasakian manifolds with respect to quarter-symmetric metric connection,Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 54, 2, 21-40, (2015).
• A. Friedmann and J. A. Schouten, Uber die Geometrie der halbsymmetrischen Ubertragungen,Mathematische Zeitschrift., 21(1) 211223, (1924).
• S. Golab,On semi-symmetric and quarter-symmetric linear connections,The Tensor Society., 22(3), 293-301,(1975).
• H. A. Hayden,Subspaces of a space with torsion,Proceedings London Mathematical Society., 34, 27-50, (1932).
• R. S. Mishra and S. N. Pandey, On quarter-connections metric F-connections,The Tensor Society., 34(1), 1-7, (1980).
• A. K. Mondal and U. C. De, Some properties of a quarter-symmetric metric connection on a Sasakian manifold, Bulletin of Mathematical Analysis and Applications., 1(3), 99-108, (2009).
• C. Patra and A. Bhattacharyya,Quarter-symmetric metric connection on pseudosymmetric Lorentzian α -Sasakian manifolds, International J.Math. Combin. 1, 46-59, (2013).
• K. T. Pradeep Kumar, C. S. Bagewadi, and Venkatesha, On projective ö-symmetric K-contact manifold admitting quarter- symmetric metric connection, Differential Geometry Dynamical Systems., 13, 128-137, (2011).
• K. T. Pradeep Kumar, Venkatesha, and C.S.Bagewadi,On φ -Recurrent Para-Sasakian Manifold Admitting Quarter-Symmetric, Metric Connection,ISRN Geometry., Article ID 317253, 10 pages doi:10.5402, (2012).
• S. C. Rastogi, On quarter-symmetric metric connection,Comptes Rendus de l’Academie Bulgare des Sciences., 31(7), 811-814, (1978).
• S. C. Rastogi, On quarter-symmetric metric connections,The Tensor Society, vol. 44, no. 2, pp. 133 141, (1987).
• T. Takahashi, Sasakian φ -symmetric spaces,Tohoku math J., 29, 91-113, (1977).
• Venkatesha, K.T.P. Kumar and C.S. Bagewadi, On Quarter-Symmetric Metric Connection in a Lorentzian Para-Sasakian, Manifold, Azerbaijan Journal of Mathematics., 5(1), 3-12, (2015).
• S. Yadav and D. L. Suthar, Certain derivation on Lorentzian α -Sasakian manifolds,Mathematics and Decision Science 12 (2012).
• K. Yano, On semi-symmetric metric connection, Revue Roumaine de Mathematiques Pures et Appliqu’ees., 15, 1579-1586, (1970).
• K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors, The Tensor Society., 38, 13-18, (1982).
• K. Yano and M. Kon, Structures on manifolds, volume 3 of Series in Pure Mathematics, World Scientific Publishing Co.,Singapore, (1984).
• Yildiz A, Murathan C, On Lorentzian α -Sasakian manifolds, Kyungpook Math. J. 45, 95-103, (2005).
• A. Yildiz and M. Turan,A Class of Lorentzian α -Sasakian Manifolds,Kyungpook Math. J. 49, 789-799, (2009).
• A. Yildiz, U. C. De and Erhan Ata,On a type of Lorentzian α -Sasakian manifolds,MATH. REPORTS, 16(66), 1, 61-67, (2014).