• Honam Mathematical Journal
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• v.35 no.2
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• pp.119-128
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• 2013

In the present paper, we define a product-symmetric recurrent-metric connection in an almost Hermitian manifold and study some properties of this connection, in particular, its curvature properties.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.897-906
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• 2024

On a Hermitian manifold, the Chern connection can induce a metric connection on the background Riemannian manifold. We call the sectional curvature of the metric connection induced by the Chern connection the Chern sectional curvature of this Hermitian manifold. First, we derive expression of the Chern sectional curvature in local complex coordinates. As an application, we find that a Hermitian metric is Kähler if the Riemann sectional curvature and the Chern sectional curvature coincide. As subsequent results, Ricci curvature and scalar curvature of the metric connection induced by the Chern connection are obtained.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.455-463
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• 1996

In [3] and [4], Kitahara, Pak and the author obtained the conformally invariant tensor $B_0$, which is an algebraic Hermitian analogue of the Weyl conformal curvature tensor W in the Riemannian geometry, by the decomposition of the curvature tensor H of the Hermitian connection and the notion of semi-curvature-like tensors of Tanno (see[7]). In [5], the author defined a conformally invariant tensor $B_0$ on a Hermitian manifold as a modification of $B_0$. Moreover he introduced the notion of local conformal Hermitian-flatness of Hermitian manifolds and proved that the vanishing of this tensor $B_0$ together with some condition for the scalar curvatures is a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.375-384
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• 1995

The almost Hermitian Finsler structure of a Rizza manifold is an almost Hermitian structure if a special condition satisfies. In this paper, the induced Finsler connection from Moor metric is define and the some properties of a Kaehlerian Finsler manifold with respect to the induced Finsler connection from Moor metric are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.725-733
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• 2011

The characteristic connection is a good substitute for the Levi-Civita connection, especially in studying non-integrable geometries. Unfortunately, not every geometric structure has the characteristic connection. In this paper we consider the space $U(3)/(U(1){\times}U(1){\times}U(1))$ with an almost Hermitian structure and prove that it has a geometric structure admitting the characteristic connection.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1237-1246
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• 2016

In this paper we study some properties of submanifolds of a Riemannian manifold equipped with a generalized connection $\hat{\nabla}$. We also consider almost Hermitian manifolds that admits a special case of this generalized connection and derive some results about the behavior of this manifolds.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1423-1438
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• 2022

In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1269-1281
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• 2020

In this article, we show that a pseudo-Hermitian magnetic curve in a normal almost contact metric 3-manifold equipped with the canonical affine connection ${\hat{\nabla}}^t$ is a slant helix with pseudo-Hermitian curvature ${\hat{\kappa}}={\mid}q{\mid}\;sin\;{\theta}$ and pseudo-Hermitian torsion ${\hat{\tau}}=q\;cos\;{\theta}$. Moreover, we prove that every pseudo-Hermitian magnetic curve in normal almost contact metric 3-manifolds except quasi-Sasakian 3-manifolds is a slant helix as a Riemannian geometric sense. On the other hand we will show that a pseudo-Hermitian magnetic curve γ in a quasi-Sasakian 3-manifold M is a slant curve with curvature κ = |(t - α) cos θ + q| sin θ and torsion τ = α + {(t - α) cos θ + q} cos θ. These curves are not helices, in general. Note that if the ambient space M is an α-Sasakian 3-manifold, then γ is a slant helix.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.599-608
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• 2012

In [2], [8], the author studied the characteristic connection as a good substitute for the Levi-Civita connection. In this paper, we consider the space $U(3)=(U(1){\times}U(1){\times}U(1))$ with an almost Hermitian structure which admits a characteristic connection and compute the characteristic connection concretely.