3-Dimensional Quasi-Sasakian Manifolds with Semi-Symmetric Non-Metric Connection FULL TEXT

Year 2012, Volume: 41 Issue: 1, 127 - 137, 01.01.2012

Uday C. De Ahmet Yildiz Mine Turan Bilal E. Acet

Keywords

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References

• Agashe, N. S. and Chafle, M. R. A semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 23 (6), 399–409, 1992
• Amur, K. and Pujar, S. S. Submanifolds of a Riemannian manifold with semi-symmetric metric connection, Tensor N. S. 32, 35–38, 1978.
• Ahsan, Z. and Siddiqui, S. A. Concircular curvature tensor and fluid spacetimes, Interna- tional Journal of Theo. Physics 48, 3202–3212, 2009.
• Blair, D. E. Contact Manifolds in Riemannian Geometry (Lecture Notes in Mathematics , Springer-Verlag, Berlin-New York, 1976).
• Blair, D. E. Riemannian Geometry of Contact and Symplectic Manifolds (Progress in Math- ematics 203, Birkhauser Inc., Boston, 2002).
• Blair, D. E., The theory of quasi-Sasakian structure, J. Differential Geo. 1, 331-345, 1967.
• Blair, D. E., Kim, J. S. and Tripathi, M. M. On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc. 42, 883-892, 2005.
• Cabrerizo, J. L., Fernandez, L. M., Fernandez, M. and Zhen, G. The structure of a class of K-contact manifolds, Acta Math. Hungar. 82 (4), 331–340, 1999.
• Das, L., De, U. C., Singh, R. N. and Pandey, M. K. Lorentzian manifold admitting a type of semi-symmetric non-metric connection, Tensor N. S. 70, 78–85, 2008.
• De, U. C. On a type of semi-symmetric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 2 (1), 334–338, 1990.
• De, U. C. On a type of semi-symmetric connection on a Riemannian manifold, Ann. Stiint Univ. Al. I. Cuza Iasi Sect. Math. 37, 105–108, 1991.
• Friedmann, A. and Schouten, J. A. ¨Uber die Geometrie der halbsymmetrischen ¨Ubertragun- gen, Math. Z. 21 (1), 211–223, 1924.
• Gonzalez, J. C. and Chinea, D. Quasi-Sasakian homogeneous structures on the generalized Heisenberg group H(p, 1), Proc. Amer. Math. Soc. 105, 173–184, 1989.
• Hayden, H. A. Subspace of a space with torsion, Proc. London Math. Soc. 34, 27–50, 1932.
• Imai, T. Notes on semi-symmetric metric connections, Tensor N. S. 24, 293–96, 1972.
• Kim, B. H. Fibred Riemannian spaces with quasi-Sasakian structure, Hiroshima Math. J. , 477–513, 1990.
• Kanemaki, S. Quasi-Sasakian manifolds, Tohoku Math. J. 29, 227–233, 1977.
• Kanemaki, S. On quasi-Sasakian manifolds, Differential Geometry Banach Center Publica- tions 12, 95–125, 1984.
• Liang, Y. On semi-symmetric recurrent metric connection, Tensor N. S. 55, 107–102, 1994.
• Nakao, Z. Submanifolds of a Riemannian manifold with semi-symmetric metric connection, Proc. Am. Math. Soc. 54, 261–66, 1976.
• Oubina, J. A. New classes of almost contact metric structures, Publ. Math. Debrecen 32, –193, 1985.
• Olszak, Z. Normal almost contact metric manifolds of dimension 3, Ann. Polon. Math. 47, –50, 1986.
• Olszak, Z. On three dimensional conformally flat quasi-Sasakian manifold, Period Math. Hungar. 33 (2), 105–113, 1996.
• Pravonovic, M. On pseudo symmetric semi-symmetric connection, Pub. De L’ Institu Math., Nouvelle Serie, 18 (32), 157–164, 1975.
• Schouten, J. A. Ricci-calculus (Springer-Verlag, Berlin, 1954).
• Sengupta, J., De, U. C. and Binh, T. Q. On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 31, 1659–1670, 2000.
• Takahashi, T. Sasakian φ-symmetric spaces, Tohoku Math. J. 29, 91–113, 1977.
• Tanno, S. Quasi-Sasalian structure of rank 2p + 1, J. Differential Geom. 5, 317–324, 1971.
• Yano, K. Integral formulas in Riemannian Geometry (Marcel Dekker Inc., New York, 1970).
• Yano, K. and Kon, M. Structures on Manifolds (World Scientific, Singapore, 1984).
• Yano, K. On semi-symmetric φ-connection in a Sasakian manifold, Kodai Math. Sem. rep. , 150–158, 1977.
• Zhen, G., Cabrerizo, J. L., Fernandez, L. M. and Fernandez, M. On ξ-conformally flat con- tact metric manifolds, Indian J. Pure Appl. Math. 28, 725–734, 1997.