• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.183-194
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• 2008

We prove that totally umbilical submanifold M of an extended quasi-recurren manifold is also extended quasi-recurrent. If, moreover, M is conformally flat then, locally, M is isometric to the manifold with known metric. Some curvature properties of such submanifold are investigated. Making use of these results we shall prove the existence of totally umbilical submanifold being pseudosymmetric in the sense of Ryszard Deszcz and satisfying some other curvature conditions.

• Bulletin of the Korean Mathematical Society
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• v.21 no.1
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• pp.21-26
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• 1984

The notion of nearly Sasakian manifold was introduced in [1] and Z-Olszak has studied certain properties in [2] and [3]. In section (2) of this paper, we show that a nearly Sasakian manifold M admitting .GAMMA.$_{ji}$ $^{h}$ such that .del.$_{1}$ $R_{kji}$$^{h}$ =0 is of contant scalar curvature and the covariant derivate of the Ricci tensor of M is a symmetric tensor. In the last section, we shall deal with a recurrent and conformal recurrent nearly Sasakian manifold.d.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.177-186
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• 2017

In this paper, a type of Riemannian manifold (namely, pseudo semiconformally symmetric manifold) is introduced. Also the several geometric properties of such a manifold is investigated. Finally the existence of such a manifold is ensured by a proper example.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.201-210
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• 2024

This paper is concerned with the study of spacetimes satisfying div 𝓜 = 0, where "div" denotes the divergence and 𝓜 is the m-projective curvature tensor. We establish that a perfect fluid spacetime with div 𝓜 = 0 is a generalized Robertson-Walker spacetime and vorticity free; whereas a four-dimensional perfect fluid spacetime becomes a Robertson-Walker spacetime. Moreover, we establish that a Ricci recurrent spacetime with div 𝓜 = 0 represents a generalized Robertson-Walker spacetime.