• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.537-562
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• 2019

The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.9-17
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• 1997

Define $\bar{g}{\upsilon, \omega) = -\upsilon_1\omega_1 + \cdots + \upsilon_n\omega_n$ for $\upsilon, \omega in R^n$. $R^n$ together with this metric is called the Lorentzian n-space, denoted by $L^n$, and $R^n$ together with the Euclidean metric is called the Euclidean n-space, denoted by $E^n$. A Lorentzian surface in $L^n$ means an orientable connected 2-dimensional Lorentzian submanifold of $L^n$ equipped with the induced Lorentzian metrix g from $\bar{g}$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.25-32
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• 2012

We define a quarter symmetric metric connection in a Lorentzia para-Sasakian manifold and study CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a quarter symmetric metric connection. Moreover, we also obtain integrability conditions of the distributions on CR-submanifolds.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.831-842
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• 2022

In this work we classified translation invariant surfaces with zero Gaussian curvature in the 3-dimensional Sol Lie group endowed with Lorentzian metric.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1133-1147
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• 2019

In this paper, let M = B×_f² F be an Einstein Lorentzian warped product manifold with 2-dimensional base. We study the geodesic completeness of some metric with constant curvature. First of all, we discuss the existence of nonconstant warping functions on M. As the results, we have some metric g admits nonconstant warping functions f. Finally, we consider the geodesic completeness on M.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.951-962
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• 2003

In this paper we address focal points and treat manifolds (M, g) whose Lorentzian metric tensors g have a spacelike $C^{0}$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1$-geodesics. The condition of maximality of timelike curves(geodesics) passing $C^{0}$-hypersurface is studied.ied.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.641-648
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• 2000

The purpose of this paper is to give a necessary and sufficient condition for a smooth manifold to admit a Lorentzian metric. As an application of this result, on Lorentzian manifolds we have shown that the existence of a 1-dimensional distribution is equivalent to the existence of a non-vanishing vector field.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.447-456
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• 2018

In this paper, we consider nonconstant warping functions on Einstein Lorentzian warped product manifolds $M=B{\times}_{f^2}F$ with an 1-dimensional base B which has a negative definite metric. As the results, we discuss that on M the resulting Einstein Lorentzian warped product metric is a future (or past) geodesically complete one outside a compact set.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.281-293
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• 2019

In the present paper, we study quasi-concircular curvature tensor satisfying certain curvature conditions on a Lorentzian ${\beta}$-Kenmotsu manifold with respect to the semi-symmetric semi-metric connection.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.339-359
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• 2022

In this paper, we investigate k-Ricci curvature and k-scalar curvature on lightlike hypersurfaces of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using this curvatures, we establish some inequalities for screen homothetic lightlike hypersurface of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using these inequalities, we obtain some characterizations for such hypersurfaces. Considering the equality case, we obtain some results.