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

Santu DEY;  Buddhadev Pal;  Arindam 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 Pahan;  Buddhadev Pal;  Arindam 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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