• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.189-200
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• 1999

In this paper, we proved that the only surfaces of 1-type Gauss map with flat normal connection are spheres, products of two plane circles and helical cylinders.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1033-1045
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• 2017

The conharmonic curvature tensor under certain conditions has been studied for Kenmotsu manifolds with respect to the semi-symmetric metric connection.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.636-645
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• 2022

We find a 1-parameter family of homogeneous structure tensors on contact hypersurfaces in Hermitian symmetric spaces. Among their associated Ambrose-Singer connections, we prove that the TanakaWebster connection is the unique pseudo-homothetically invariant connection.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.3
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• pp.163-169
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• 2023

In this article, we consider a vectorial linear connection which is determined by three fixed vector fields. Classifying these vectorial connections, we obtain a new type of generalized statistical manifolds which allow non-zero torsion.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1249-1260
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• 2023

In the present paper, we study a semi-symmetric recurrent metric connection and verify its various geometric properties.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.175-186
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• 2024

In this paper, we study para-Kenmotsu manifolds admitting generalized η-Ricci solitons associated to the Zamkovoy connection. We provide an example of generalized η-Ricci soliton on a para-Kenmotsu manifold to prove our results.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1101-1113
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• 2014

We give analogous criterion to admit a real parabolic connection on real parabolic bundles over a real curve. As an application of this criterion, if real curve has a real point, then we proved that a real vector bundle E of rank r and degree d with gcd(r, d) = 1 is real indecomposable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by $-\frac{d}{r}$. We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.

• 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.36 no.1
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• pp.149-164
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• 2021

By using a statistical connection, we define a semi-symmetric metric connection on statistical manifolds and study the geometry of these manifolds and their submanifolds. We show the symmetry properties of the curvature tensor with respect to the semi-symmetric metric connections. Also, we prove the induced connection on a submanifold with respect to a semi-symmetric metric connection is a semi-symmetric metric connection and the second fundamental form coincides with the second fundamental form of the Levi-Civita connection. Furthermore, we obtain the Gauss, Codazzi and Ricci equations with respect to the new connection. Finally, we construct non-trivial examples of statistical manifolds admitting a semi-symmetric metric connection.