In the present paper, we have defined a Hsu-unified structure manifold and a Hsu-Kahler manifold and studied some properties of the quarter-symmetric non-metric connection. Certain interesting results on such manifolds have been obtained. We have also studied the properties of the contravariant almost analytic vector field on these manifolds equipped with the quarter-symmetric non-metric connection.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 3)

Pages:

63-70

Citation:

R. Nivas and A. Agnihotri, "On a Hsu-Unified Structure Manifold with a Quarter-Symmetric Non-Metric Connection", Bulletin of Mathematical Sciences and Applications, Vol. 3, pp. 63-70, 2013

Online since:

February 2013

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Open Access

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Creative Commons Attribution 4.0 International License

References:

Golab, S. (1975): On semi-symmetric and quarter-symmetric linear connections, Tensor N. S., Vol. 29, pp.249-254.

Kobayashi, S. and Nomizu, K. (1969): Foundation of differential geometry, Vol. I and II, Interscience Publisher, London.

Mishra, R. S. (1984): Structures on a differentiable manifold and their applications, Chandrama Prakashan, 50-A Balrampur House, Allahabad, India. (6. 7) (6. 8) (6. 9) (6. 10) (6. 11) (6. 12) (6. 13) (6. 14).

Mondal, A. K. and De, U. C. (2009): Some properties of a Quarter-symmetric metric connection on a Sasakian manifold, Bull. Math. Anal. Appl., Vol. 1, Issue 3, pp.99-108.

Mukhopadhyay, S., Roy, A. K. and Barua, B. (1991): Some properties of a quarter- symmetric metric connection on a Riemannian manifold, Soochow J. of Math., Vol. 17 (2), pp.205-211.

Singh, B. P. (2005): Hypersurfaces of a unified structure manifold, Acta Ciencia Indica, Vol. XXXI (2), pp.487-490.

Sengupta, J. and Biswas, B. (2003): Quarter-symmetric non-metric connection on a Sasakian manifold, Bull. Cal. Math. Soc., Vol. 95(2), pp.169-176.

Sular, S., Ozgur, C. and De, U. C. (2008): Quarter-symmetric metric connection in a Kenmotsu manifold, SUT. J. Math., Vol. 44 (2), pp.297-306.

Singh, R. N. and Pandey, M. K. (2007): On a type of quarter-symmetric non-metric connection in a Kenmotsu manifold, Bull. Cal. Math. Soc., vol. 99 (4), pp.433-444.

Yano K. and Imai, T. (1982): Quarter-symmetric metric connections and their curvature tensors, Tensor N. S., Vol. 38, pp.13-18.

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