• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.301-309
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• 1995

Manifolds with recurrent connections have been studied by many authors, such as Chung, Datta, E.M.Patterson, M.Prvanovitch, Singal, and TAkano, etc (refer to [2] and [3]). Examples of such manifolds are those of recurrent curvature, Ricci-recurrent manifolds, and birecurrent manifolds.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.449-461
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• 2009

The object of the present paper is to study $(LCS)_n$-manifolds. Several interesting results on a $(LCS)_n$-manifold are obtained. Also the generalized Ricci recurrent $(LCS)_n$-manifolds are studied. The existence of such a manifold is ensured by several non-trivial new examples.

• 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.34 no.4
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• pp.1315-1328
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• 2019

The object of the present paper is to study ${\eta}$-recurrent ${\ast}$-Ricci tensor, ${\ast}$-Ricci semisymmetric and globally ${\varphi}-{\ast}$-Ricci symmetric contact metric generalized (${\kappa}$, ${\mu}$)-space form. Besides these, ${\ast}$-Ricci soliton and gradient ${\ast}$-Ricci soliton in contact metric generalized (${\kappa}$, ${\mu}$)-space form have been studied.

• 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.

• 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.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1249-1260
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• 2023

In the present paper, we study a semi-symmetric recurrent metric connection and verify its various geometric properties.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.53-68
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• 2017

The object of the present paper is to study generalized Z-recurrent manifolds. Some geometric properties of generalized Z-recurrent manifolds have been studied under certain curvature conditions. Finally, we give an example of a generalized Z-recurrent manifold.