• East Asian mathematical journal
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• v.22 no.1
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• pp.111-130
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• 2006

We study cosymplectic submersions with vanishing cosymplectic Bochner curvature tensor.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.375-395
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• 2022

We define an almost Norden submersion (holomorphic and semi-Riemannian submersion) between almost Norden manifolds and show that, in most of the cases, the base manifold has the similar kind of structure as that of total manifold. We obtain necessary and sufficient conditions for almost Norden submersion to be a totally geodesic map. We also derive decomposition theorems for the total manifold of such submersions. Moreover, we study the harmonicity of almost Norden submersions between almost Norden manifolds and between Kaehler-Norden manifolds. Finally, we derive conditions for an almost Norden submersion to be a harmonic morphism.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.951-962
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• 2013

We introduce semi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions, etc. We obtain characterizations, investigate the integrability of distributions and the geometry of foliations, etc. We also find a condition for such submersions to be harmonic. Moreover, we give lots of examples.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.637-655
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• 2019

In this paper, we introduce conformal semi-slant submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds. We investigate integrability of distributions and the geometry of leaves of such submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds. Moreover, we examine necessary and sufficient conditions for such submersions to be totally geodesic where characteristic vector field ${\xi}$ is vertical.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.599-620
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• 2023

In this paper, h-quasi-hemi-slant submersions and almost h-quasi-hemi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds are introduced. Fundamental results on h-quasi-hemi-slant submersions: the integrability of distributions, geometry of foliations and the conditions for such submersions to be totally geodesic are investigated. Moreover, some non-trivial examples of the h-quasi-hemi-slant submersion are constructed.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.205-221
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• 2023

The main goal of the paper is the introduction of the notion of conformal hemi-slant submersions from almost contact metric manifolds onto Riemannian manifolds. It is a generalization of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. Our main focus is conformal hemi-slant submersion from cosymplectic manifolds. We tend also study the integrability of the distributions involved in the definition of the submersions and the geometry of their leaves. Moreover, we get necessary and sufficient conditions for these submersions to be totally geodesic, and provide some representative examples of conformal hemi-slant submersions.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1407-1419
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• 2021

The Iwasawa decomposition NAK of the Lie group G = SO₀(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially in the first case, the base space has a constant curvature 0; the holonomy displacement along a (null-homotopic) simple closed curve in the base space is determined only by the Euclidean area of the region surrounded by the curve.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.999-1018
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• 2020

In this paper, our main objective is to introduce the notion of conformal hemi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalized case of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. We mainly focus on conformal hemi-slant submersions from Kähler manifolds. During this manner, we tend to study and investigate integrability of the distributions which are arisen from the definition of the submersions and the geometry of leaves of such distributions. Moreover, we tend to get necessary and sufficient conditions for these submersions to be totally geodesic for such manifolds. We also provide some quality examples of conformal hemi-slant submersions.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.789-796
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• 1996

A complete open manifold with nonnegative curvature is diffeomorphic to the normal bundle of the soul, and the projection map is a Riemannian submersion. Under certain circumstances, we prove that a harmonic map from a compact manifold followed by the projection is again harmonic. Therefore we obtain a harmonic map onto the soul when there is a harmonic map into an open manifold.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.13-33
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• 2006

In this article, we study the relations of horizontally conformal maps and harmonic morphisms with the stability of minimal fibers. Let ${\varphi}:(M^n,g){\rightarrow}(N^m,h)$ be a horizontally conformal submersion. There is a tensor T measuring minimality or totally geodesics of fibers of ${\varphi}$. We prove that if T is parallel and the horizontal distribution is integrable, then any minimal fiber of ${\varphi}$ is volume-stable. As a corollary, we obtain that any fiber of a submersive harmonic morphism whose fibers are totally geodesics and the horizontal distribution is integrable is volume-stable. As a consequence, we obtain if ${\varphi}:(M^n,g){\rightarrow}(N^2,h)$ is a submersive harmonic morphism of minimal fibers from a compact Riemannian manifold M into a surface N, T is parallel and the horizontal distribution is integrable, then ${\varphi}$ is energy-stable.