• 대한수학회지
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• 제55권1호
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• pp.161-174
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• 2018

The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci solitons where the potential vector field X is point wise collinear with the Reeb vector field ${\xi}$ of the contact metric structure.

• 호남수학학술지
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• 제30권4호
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• pp.603-616
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• 2008

A generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection which is both Einstein's equation and of the form(3.1) is called $^*g$-ME-manifold and we denote it by $^*g-MEX_n$. In this paper, we prove a necessary and sufficient condition for the existence of $^*g$-ME-connection and derive a surveyable tensorial representation of the $^*g$-ME-connection and the $^*g$-ME-vector in $^*g-MEX_n$.

• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권1호
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• pp.39-50
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• 2014

In this paper, we study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection, whose structure vector field ${\zeta}$ is tangent to M. The main result is a classification theorem for such Einstein half lightlike submanifolds of a Lorentzian space form admitting a semi-symmetric non-metric connection.

• 대한수학회논문집
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• 제32권2호
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• pp.401-416
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• 2017

The aim of this paper is to investigate locally ${\phi}-conformally$ symmetric almost Kenmotsu manifolds with its characteristic vector field ${\xi}$ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ${\xi}$ belongs to the $(k,\;{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.547-554
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• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.

• 대한수학회논문집
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• 제33권2호
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• pp.571-580
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• 2018

The object of the present paper is to prove the non-existence of pseudo projective Ricci symmetric spacetimes $(PW\;RS)_4$ with different types of energy momentum tensor. We also discuss whether a fluid $(PW\;RS)_4$ spacetime with the basic vector field as the velocity vector field of the fluid can admit heat flux. Next we consider perfect fluid and dust fluid $(PW\;RS)_4$ spacetimes respectively. Finally we construct an example of a $(PW\;RS)_4$ spacetime.

• 대한수학회보
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• 제55권1호
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• pp.227-237
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• 2018

In this paper, we study some geometric structures of a weakly cyclic Z-symmetric manifold (briefly, $[W CZS]_n$). More precisely, we prove that a conformally flat $[W CZS]_n$ satisfying certain conditions is special conformally flat and hence the manifold can be isometrically immersed in an Euclidean manifold $E^n+1$ as a hypersurface if the manifold is simply connected. Also we show that there exists a $[W CZS]_4$ with one parameter family of its associated 1-forms.

• 대한수학회지
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• 제55권2호
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• pp.391-413
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• 2018

In this paper we introduce a new tensor named semi-projective curvature tensor which generalizes the projective curvature tensor. First we deduce some basic geometric properties of semi-projective curvature tensor. Then we study pseudo semi-projective symmetric manifolds $(PSPS)_n$ which recover some known results of Chaki [5]. We provide several interesting results. Among others we prove that in a $(PSPS)_n$ if the associated vector field ${\rho}$ is a unit parallel vector field, then either the manifold reduces to a pseudosymmetric manifold or pseudo projective symmetric manifold. Moreover we deal with semi-projectively flat perfect fluid and dust fluid spacetimes respectively. As a consequence we obtain some important theorems. Next we consider the decomposability of $(PSPS)_n$. Finally, we construct a non-trivial Lorentzian metric of $(PSPS)_4$.

• 대한수학회지
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• 제53권5호
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• pp.1101-1114
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• 2016

Let ($M^{2n+1}$, ${\phi}$, ${\xi}$, ${\eta}$, g) be a (k, ${\mu}$)'-almost Kenmotsu manifold with k < -1 which admits a gradient Ricci almost soliton (g, f, ${\lambda}$), where ${\lambda}$ is the soliton function and f is the potential function. In this paper, it is proved that ${\lambda}$ is a constant and this implies that $M^{2n+1}$ is locally isometric to a rigid gradient Ricci soliton ${\mathbb{H}}^{n+1}(-4){\times}{\mathbb{R}}^n$, and the soliton is expanding with ${\lambda}=-4n$. Moreover, if a three dimensional Kenmotsu manifold admits a gradient Ricci almost soliton, then either it is of constant sectional curvature -1 or the potential vector field is pointwise colinear with the Reeb vector field.