• 호남수학학술지
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• 제41권4호
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• pp.769-780
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• 2019

We introduce anti-invariant Riemannian submersions from almost paracontact Riemannian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions.

• 호남수학학술지
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• 제45권1호
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• pp.109-122
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• 2023

In the present article, we introduce pointwise slant Riemannian submersion from nearly Kähler manifold to Riemannian manifold. We established the conditions for fibers to be totally geodesic. We also find necessary and sufficient conditions for pointwise slant submersion 𝜑 to be a harmonic and totally geodesic. Further, we study clairaut pointwise slant Riemannian submersion from nearly Kähler manifold to Riemannian manifold. We derive the clairaut conditions for 𝜑 such that 𝜑 is a clairaut map. Finally, one example is constructed which demonstrates existence of clairaut pointwise slant submersion from nearly Kähler manifold to Riemannian manifold.

• 대한수학회논문집
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• 제37권4호
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• pp.1199-1207
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• 2022

In the present paper, a Riemannian submersion 𝜋 between Riemannian manifolds such that the total space of 𝜋 endowed with a torse-forming vector field 𝜈 is studied. Some remarkable results of such a submersion whose total space is Ricci soliton are given. Moreover, some characterizations about any fiber of 𝜋 or the base manifold B to be an almost quasi-Einstein are obtained.

• 대한수학회보
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• 제51권6호
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• pp.1749-1771
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• 2014

In this paper, we introduce slant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We obtain some results on slant Riemannian submersions of a cosymplectic manifold. We also give examples and inequalities between the scalar curvature and squared mean curvature of fibres of such slant submersions in the cases where the characteristic vector field is vertical or horizontal.

• 대한수학회보
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• 제60권5호
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• pp.1155-1179
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• 2023

Main objective of the present paper is to establish Chen inequalities for slant Riemannian submersions in contact geometry. In this manner, we give some examples for slant Riemannian submersions and also investigate some curvature relations between the total space, the base space and fibers. Moreover, we establish Chen-Ricci inequalities on the vertical and the horizontal distributions for slant Riemannian submersions from Sasakian space forms.

• 충청수학회지
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• 제24권2호
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• pp.239-245
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• 2011

In this paper, we will study the tension field of the function related to a Riemannain submersion ${\pi}\;:\;N{\rightarrow}M$ with totally geodesic fibres. In case that the Riemannain submersion ${\pi}\;:\;N{\rightarrow}M$ particularly has a smooth map $f\;:\;M{\rightarrow}N$ which happens to be a section, we will show that tension field ${\tau}(f)$ of the energy functional can be decomposed into the horizontal and vertical parts.

• 대한수학회보
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• 제33권3호
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• pp.477-480
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• 1996

Let $\pi : Z \longrightarrow Y$ be a fiber bundle where Y and Z are compact Riemannian manifolds without boundary. We are primarily interested in the case where $\pi$ is a Riemannian submersion with minimal fibers; this is the case, for example, where Z is the sphere bundle of some vector bundle over Y or where Z is a principal bundle over Y.

• 호남수학학술지
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• 제44권3호
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• pp.370-383
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• 2022

In this paper, bi-slant pseudo-Riemannian submersions from para-Kaehler manifolds onto pseudo-Riemannian manifolds are introduced. We examine some geometric properties of three types of bi-slant submersions. We give non-trivial examples of such submersions. Moreover, we obtain curvature relations between the base space, total space and the fibers.

• 대한수학회논문집
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• 제36권1호
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• pp.173-187
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• 2021

In this paper, we deal with the notion of a v-semi-slant submersion from an almost Hermitian manifold onto a Riemannian manifold. We investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. Given such a map with totally umbilical fibers, we have a condition for the fibers of the map to be minimal. We also obtain an inequality of a proper v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and a v-semi-slant angle. Moreover, we give some examples of such maps and some open problems.

• 호남수학학술지
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• 제45권2호
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• pp.248-268
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• 2023

As a generalization of conformal semi-invariant submersion, conformal slant submersion and conformal semi-slant submersion, in this paper we study conformal hemi-slant submersion from Kenmotsu manifold onto a Riemannian manifold. The necessary and sufficient conditions for the integrability and totally geodesicness of distributions are discussed. Moreover, we have obtained sufficient condition for a conformal hemi-slant submersion to be a homothetic map. The condition for a total manifold of the submersion to be twisted product is studied, followed by other decomposition theorems.