• Honam Mathematical Journal
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• v.42 no.4
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• pp.733-745
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• 2020

The object of the present paper is to study the almost Hermitian submersion from an almost Hermitian manifold admits a Ricci soliton. Where, we investigate any fibre of such a submersion is a Ricci soliton or Einstein. We also get necessary conditions for which the base manifold of an almost Hermitian submersion is a Ricci soliton or Einstein. Moreover, we obtain the harmonicity of an almost Hermitian submersion from a Ricci soliton to an almost Hermitian manifold.

• 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.

• 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.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.681-694
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• 2007

We study curvature properties of four-dimensional almost Hermitian manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. We give some structure theorems for such manifolds.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.649-658
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• 1994

The notion of the almost Hermitian Finsler manifold admitting an almost complex structure $f^i_j(x)$ was, for the first time, introduced by G. B. Rizza [8]. It is known that the almost Hermitian Finsler manifold (or a Rizza manifold) has been studied by Y. Ichijyo [2] and H. Hukui [1]. In those papers, the almost Hermitian Finsler manifold which the h-covariant derivative of the almost complex structure $f^i_j(x)$ with respect to the Cartan's Finsler connection vanishes was defined as the Kaehlerian Finsler manifold. The nearly Kaehlerian Finsler manifold was defined and studied by the former of authors [7]. The present paper is the continued study of above paper.

• 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.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.817-827
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• 2021

In this paper, we prove that a diffeomorphism f on a normal almost contact 3-manifold M is a CRL-transformation if and only if M is an α-Sasakian manifold. Moreover, we show that a CR-loxodrome in an α-Sasakian 3-manifold is a pseudo-Hermitian magnetic curve with a strength $q={\tilde{r}}{\eta}({\gamma}^{\prime})=(r+{\alpha}-t){\eta}({\gamma}^{\prime})$ for constant 𝜂(𝛄'). A non-geodesic CR-loxodrome is a non-Legendre slant helix. Next, we prove that let M be an α-Sasakian 3-manifold such that (∇_YS)X = 0 for vector fields Y to be orthogonal to ξ, then the Ricci tensor 𝜌 satisfies 𝜌 = 2α²g. Moreover, using the CRL-transformation $\tilde{\nabla}^t$ we fine the pseudo-Hermitian curvature $\tilde{R}$, the pseudo-Ricci tensor $\tilde{\rho}$ and the torsion tensor field $\tilde{T}^t(\tilde{S}X,Y)$.

• 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.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.121-136
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• 1996

Met $\tilde{M} = (\tilde{M}, \tilde{J}, <>)$ be an almost Hermitian manifold and M a submanifold of $\tilde{M}$. According to the behavior of the tangent bundle TM with respect to the action of $\tilde{J}$, we have two typical classes of submanifolds. One of them is the class of almost complex submanifolds and another is the class of totally real submanifolds. In 1990, B. Y. Chen [4], [5] introduced the concept of the class of slant submanifolds which involve the above two classes. He used the Wirtinger angle to measure the behavior of TM with respect to the action of $\tilde{J}$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1115-1126
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• 2014

The purpose of this paper is to study pointwise slant submersions from almost Hermitian manifolds which extends slant submersion in a natural way. Several basic results in this point of view are proven in this paper.