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Some Properties of Lorentzian α -Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection

Santu DEYArindam BHATTACHARYYA — 2015

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric, semi-generalized recurrent, semi-generalized Ricci-recurrent Lorentzian α -Sasakian manifold with respect to quarter-symmetric metric connection. Finally, we give an example of 3-dimensional Lorentzian α -Sasakian manifold with respect to quarter-symmetric metric connection.

Conformal Ricci Soliton in Lorentzian α -Sasakian Manifolds

Tamalika DuttaNirabhra BasuArindam BHATTACHARYYA — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian α -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian α -Sasakian manifold admitting conformal Ricci soliton is η -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian α -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian α -Sasakian...

Some Classes of Lorentzian α -Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection

Santu DEYBuddhadev PalArindam BHATTACHARYYA — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian α -Sasakian manifold. We study some curvature properties of an Lorentzian α -Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally φ -symmetric, φ -symmetric, locally projective φ -symmetric, ξ -projectively flat Lorentzian α -Sasakian manifold with respect to the quarter-symmetric metric connection.

Characterization on Mixed Generalized Quasi-Einstein Manifold

Sampa PahanBuddhadev PalArindam BHATTACHARYYA — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the present paper we study characterizations of odd and even dimensional mixed generalized quasi-Einstein manifold. Next we prove that a mixed generalized quasi-Einstein manifold is a generalized quasi-Einstein manifold under a certain condition. Then we obtain three and four dimensional examples of mixed generalized quasi-Einstein manifold to ensure the existence of such manifold. Finally we establish the examples of warped product on mixed generalized quasi-Einstein manifold.

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