• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.731-739
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• 2015

The object of the present paper is to characterize a Riemannian manifold admitting a type of semi-symmetric non-metric connection.

• 호남수학학술지
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• 제45권1호
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• pp.109-122
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• 2023

In the present article, we introduce pointwise slant Riemannian submersion from nearly Kähler manifold to Riemannian manifold. We established the conditions for fibers to be totally geodesic. We also find necessary and sufficient conditions for pointwise slant submersion 𝜑 to be a harmonic and totally geodesic. Further, we study clairaut pointwise slant Riemannian submersion from nearly Kähler manifold to Riemannian manifold. We derive the clairaut conditions for 𝜑 such that 𝜑 is a clairaut map. Finally, one example is constructed which demonstrates existence of clairaut pointwise slant submersion from nearly Kähler manifold to Riemannian manifold.

• 대한수학회보
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• 제37권3호
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• pp.543-550
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• 2000

We prove that every generalized Landsberg manifold of scalar curvature R is a Riemannian manifold of constant curvature, provided that $R\neq\ 0$.

• 대한수학회보
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• 제54권1호
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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.

• 호남수학학술지
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• 제36권4호
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• pp.723-730
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• 2014

In the present paper, we introduce a type of Riemannian manifolds (namely, $W_4$-birecurrent manifold) and study the several properties of such a manifold on which some geometric conditions are imposed.

• Korean Journal of Mathematics
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• 제31권2호
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• pp.133-137
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• 2023

Consider a Riemannian manifold M equipped with a metric g. In this article, we study a notion for statistical manifolds (M, g, ∇), which can have a nonzero torsion, abbreviated to SMT. Then it turns out that the tensor fields ∇g and ${\tilde{\nabla}}g$ obtained from two different SMT-connections are different.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권4호
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• pp.327-335
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• 2012

We study half lightlike submanifolds M of semi-Riemannian manifolds $\widetilde{M}$ of quasi-constant curvatures. The main result is a characterization theorem for screen homothetic Einstein half lightlike submanifolds of a Lorentzian manifold of quasi-constant curvature subject to the conditions; (1) the curvature vector field of $\widetilde{M}$ is tangent to M, and (2) the co-screen distribution is a conformal Killing one.

• 대한수학회지
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• 제43권4호
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• pp.717-732
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• 2006

In this paper, we study both slant 3nd semi-slant sub-manifolds of an almost product Riemannian manifold. We give characterization theorems for slant and semi-slant submanifolds and investigate special class of slant submanifolds which are product version of Kaehlerian slant submanifold. We also obtain integrability conditions for the distributions which are involved in the definition of a semi-slant submanifold. Finally, we prove a theorem on the geometry of leaves of distributions under a condition.

• 대한수학회지
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• 제32권1호
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• pp.151-160
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• 1995

The notion of finite type submanifold was introduced by B.-Y. Chen [1]. A lot of works were done in this field of study by many authors. B.-Y. Chen also extended this notion to pseudo-Riemannian submanifold of pseudo-Euclidean space ([2]).

• 대한수학회지
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• 제32권1호
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• pp.93-101
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• 1995

Let (M,g) be an n-dimensional, connected Riemannian manifold with Levi Civita connection $\nabla$ and Riemannian curvature tensor R defined by $$ R_XY = [\nabla_X, \nabla_Y] - \nabla_{[X,Y]} $$ for all smooth vector fields X, Y. $\nablaR, \cdots, \nabla^kR, \cdots$ denote the successive covariant derivatives and we assume $\nabla^0R = R$.