• 대한수학회논문집
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• 제38권2호
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• pp.621-628
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• 2023

Given a linear connection ∇ and its dual connection ∇^*, we discuss the situation where ∇ + ∇^* = 0. We also discuss statistical manifolds with torsion and give new examples of some type for linear connections inducing the statistical manifolds with non-zero torsion.

• 대한수학회논문집
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• 제11권2호
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• pp.423-443
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• 1996

The main purposer of the present paper is to derive the induced (Finsler) connections on the hypersurface from the Finsler connections of Cartan type (a Wagner, Miron, Cartan C- and Cartan Y- connection) of a Finsler space and to seek the necessary and sufficient conditions that the induced connections coincide with the intrinsic connections. And we show the differences of quantities with respect to the respective a connections and an induced Cartan connection. Finally we show some examples.

• 대한수학회보
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• 제52권5호
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• pp.1631-1647
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• 2015

In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of generalized space forms endowed with a semi-symmetric metric connection. Moreover, we also characterize those submanifolds for which the equality cases hold.

• East Asian mathematical journal
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• 제19권2호
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• pp.261-271
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• 2003

We deal with two metrics of Randers type, which are characterized by the solution of certain differential equations respectively. Furthermore, we will give the condition for a Finsler space with such a metric to be a locally Minkowski space or a conformally flat space, respectively.

• 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.

• 대한수학회보
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• 제42권2호
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• pp.405-413
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• 2005

We consider the connections $\nabla$ on the Rizza manifold (M, J, L) satisfying ${\nabla}G=0\;and\;{\nabla}J=0$. Among them, we derive a Lichnerowicz connection from the Cart an connection and characterize it in terms of torsion. Generalizing Kahler condition in Hermitian geometry, we define a Kahler condition for Rizza manifolds. For such manifolds, we show that the Cartan connection and the Lichnerowicz connection coincide and that the almost complex structure J is integrable.

• 대한수학회논문집
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• 제17권3호
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• pp.505-517
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• 2002

We introduce certain conformally invariant h-Finsler connection in a Rizza manifold. Using this connection, we find some conformally invariant Finsler tensors. The conformal flatness and the Kaehlerian Finsler manifold with respect to the above connection are investigated.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권4호
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• pp.229-236
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• 2014

In this paper, we study two types of 1-lightlike submanifolds, named by lightlike hypersurface and half lightlike submanifold, of an indefinite Sasakian manifold admitting non-metric ${\theta}$-connections. We prove that there exist no such two types of 1-lightlike submanifolds of an indefinite Sasakian manifold.

• 대한수학회지
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• 제35권1호
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• 호남수학학술지
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• 제44권2호
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• pp.179-194
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• 2022

In the present study, we investigate generic lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving the existence of generic lightlike submanifolds in an indefinite generalized complex space form, a non-trivial example of this class of submanifolds is discussed. Then, we find a characterization theorem enabling the induced connection on a generic lightlike submanifold to be a metric connection. We also derive some conditions for the integrability of distributions defined on generic lightlike submanifolds. Further, we discuss the non-existence of mixed geodesic generic lightlike submanifolds in a generalized complex space form. Finally, we investigate totally umbilical generic lightlike submanifolds and minimal generic lightlike submanifolds of an indefinite nearly Kaehler manifold.