A Note On The Quasi-Conformal And M-Projective Curvature Tensor Of A Semi-Symmetric Recurrent Metric Connection On A Riemannian Manifold

Year 2013, Volume: 8 Issue: 2, 190 - 194, 05.12.2013

Rajesh Kumar Jagannath Chowdhury

Abstract

Abstract: In the present note we have considered Mn to be a Riemannian manifold admitting a semi-symmetric recurrent metric connection. The aim of the present paper is to obtain the conditions under which the quasi-conformal curvature tensor and M-projective curvature tensor of semi-symmetric recurrent metric connection and the Riemannian connection to be equal.

Key words: Semi-symmetric recurrent metric connection, quasi-conformal curvature tensor, M-projective curvature tensor.

Keywords

: Semi-symmetric recurrent metric connection, quasi-conformal curvature tensor, �-projective curvature tensor

A Note On The Quasi-Conformal And M-Projective Curvature Tensor Of A Semi-Symmetric Recurrent Metric Connection On A Riemannian Manifold

Abstract

In the present note we have considered recurrent metric connection. The aim of the present paper is to obtain the conditions under which the quasiconformal curvature tensor and -projective curvature tensor of semi-symmetric recurrent metric connection and the Riemannian connection to be equal.  to be a Riemannian manifold admitting a semi-symmetric

Keywords

Semi-symmetric recurrent metric connection, quasi-conformal curvature tensor, -projective curvature tensor

References

• [1] Eisenhart L.P., 1949. Riemannian Geometry. Princeton University Press, Princeton N.J.
• [2] Mukhopadhyay S., Barua B., 1990. A note on the projective curvature tensor of a semi-symmetric recurrent metric connection on a Riemannian manifold. Ale Universitat, “AL. I Cuza” Iasi, Tomul XXXVI, Mathematica. 415-417.
• [3] Pokhariyal G.P., Mishra R.S., 1971. Curvature tensor and their relativistic significance II. Yokohama math, Journal. 19, 97-103.
• [4] Ray A.K., Mukhopadhyay S., 1990. Semi-symmetric recurrent metric connection on a Riemannian manifold. Jour. Pure Math. (7), 35-38.
• [5] Smaranda D., Andonie O.C., 1976. On semi-symmetric connections, Ann. Fac. Sci. Univ. Nat. Zaire (Kinshasa) Sect. Math. Phys. 2, 265-270.
• [6] Yano K., Sawaki S., 1968. Riemannian manifold admitting a conformal transformation group. J. of Differential Geometry, 2, 161-184.