• Honam Mathematical Journal
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• v.45 no.3
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• pp.471-490
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• 2023

In this present paper, we study QSM-connection (quarter-symmetric metric connection) on Sasakian statistical manifolds. Firstly, we express the relation between the QSM-connection ${\tilde{\nabla}}$ and the torsion-free connection ∇ and obtain the relation between the curvature tensors ${\tilde{R}}$ of ${\tilde{\nabla}}$ and R of ∇. After then we obtain these relations for ${\tilde{\nabla}}$ and the dual connection ∇^* of ∇. Also, we give the relations between the curvature tensor ${\tilde{R}}$ of QSM-connection ${\tilde{\nabla}}$ and the curvature tensors R and R^* of the connections ∇ and ∇^* on Sasakian statistical manifolds. We obtain the relations between the Ricci tensor of QSM-connection ${\tilde{\nabla}}$ and the Ricci tensors of the connections ∇ and ∇^*. After these, we construct an example of a 3-dimensional Sasakian manifold admitting the QSM-connection in order to verify our results. Finally, we study the submanifolds with the induced connection with respect to QSM-connection of statistical manifolds.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.311-323
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• 2014

In this paper, we construct two types of non-tangential half lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. Our main result is to prove several characterization theorems for each types of such half lightlike submanifolds equipped with totally geodesic screen distributions.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.329-342
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• 2013

We study lightlike hypersurfaces M of a semi-Riemannian space form $\tilde{M}(c)$ with a semi-symmetric non-metric connection whose structure vector field is tangent to M. Our main result is two characterization theorems for such a lightlike hypersurface.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.23-31
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• 1999

The purpose of the present paper is devoted to a study of some properties on spaces with a quartic metric from the standpoint of Finsler geometry.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.809-818
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• 2013

We study irrotational half lightlike submanifolds M of a semi-Riemannian space form with a semi-symmetric non-metric connection such that its structure vector field is tangent to M. We prove two characterization theorems for such an irrotational half lightlike submanifold.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1203-1219
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• 2020

Jin [7] defined a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. He said that this connection is an (ℓ, m)-type connection. Jin also studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (ℓ, m)-type connection in [7]. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold endowed with an (ℓ, m)-type connection.

• Journal of Computing Science and Engineering
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• v.4 no.3
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• pp.225-239
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• 2010

This paper introduces a new approach to modeling relative distance among nodes under a variety of communication rates, due to node's mobility in Mobile Ad-hoc Networks (MANETs). When mobile nodes move to another location, the relative distance of communicating nodes will directly affect the data rate of transmission. The larger the distance between two communicating nodes is, the lower the rate that they can use for transferring data will be. The connection certainty of a link also changes because a node may move closer to or farther away out of the communication range of other nodes. Therefore, the stability of a route is related to connection entropy. Taking into account these issues, this paper proposes a new routing metric for MANETs. The new metric considers both link weight and route stability based on connection entropy. The problem of determining the best route is subsequently formulated as the minimization of an object function formed as a linear combination of the link weight and the connection uncertainty of that link. The simulation results show that the proposed routing metric improves end-to-end throughput and reduces the percentage of link breakages and route reparations.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.603-614
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• 2019

In the present paper, we derive two optimal inequalities for totally real submanifolds and C-totally real submanifolds of LCS-manifolds with respect to Levi-Civita connection and quarter symmetric metric connection by using T. Oprea's optimization method.

• East Asian mathematical journal
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• v.15 no.1
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• pp.81-90
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• 1999