A note on semi-symmetric metric connection in Riemannian manifold

Braj Bhushan Chaturvedi

Abstract


In this paper we have discussed the Riemannian manifolds admitting asemi-symmetric metric connection r by taking as a unit parallel vector fieldwith respect to Levi-Civita connection r. We found that the manifold M beconcircular semi-symmetric with respect to Levi-Civita connection r if and onlyif it is semi-symmetric with respect to r and M be a quasi-Einstein manifold ifit will be concircularly-flat with respect to semi-symmetric metric connection r.Also, we have shown that a semi-symmetric manifold M be a conformally-flatquasi-Einstein manifold under the condition R.C = 0 or R.C − C .R = 0 for aconcircular curvature tensor C.

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