• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.667-676
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• 2014

In this article, we study slant and semi-slant submanifolds of $(LCS)_n$-manifolds. Integrability conditions of distributions involved in definition of semi-slant submanifolds of a $(LCS)_n$-manifold have been obtained.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.141-148
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• 2012

In this paper we define the AP-$GR_{k}$ integral and investigate some properties of this integral. Also, a convergence theorem is proved using equi-integrability conditions.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.321-335
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• 2006

Generic submanifolds of a Riemannian manifold endowed with a hypercosymplectic 3-structure are studied. Integrability conditions for certain distributions on the generic submanifold are discussed. Geometry of leaves of certain distributions are also studied.

• 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.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1073-1087
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• 2022

We introduce two new classes of lightlike submersions, namely, screen slant and screen semi-slant lightlike submersions from an indefinite Kaehler manifold to a lightlike manifold giving characterization theorems with non trivial examples for both classes. Integrability conditions of all distributions related to the definitions of these submersions have been obtained.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.701-715
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• 2021

In this paper, we study almost complex Norden Silver manifolds and Kaehler-Norden Silver manifolds. We define adapted connections of first, second and third type to an almost complex Norden Silver manifold and establish the necessary and sufficient conditions for the integrability of almost complex Norden Silver structure. Moreover, we investigate that a complex Norden Silver map is a harmonic map between Kaehler-Norden Silver manifolds.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.277-291
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• 2022

The aim of this article is to examine some types of slant submanifolds of bronze Riemannian manifolds. We introduce hemi-slant submanifolds of a bronze Riemannian manifold. We obtain integrability conditions for the distribution involved in quasi hemi-slant submanifold of a bronze Riemannian manifold. Also, we give some examples about this type submanifolds.

• Honam Mathematical Journal
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• v.45 no.2
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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.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.257-273
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• 2020

We introduce and study quasi hemi-slant submanifolds of almost contact metric manifolds (especially, cosymplectic manifolds) and validate its existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant submanifolds of cosymplectic manifolds, are obtained. Also, we investigate the necessary and sufficient conditions for quasi hemi-slant submanifolds of cosymplectic manifolds to be totally geodesic and study the geometry of foliations determined by the distributions.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1091-1101
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• 2018

We concern in this paper the graph Kazdan-Warner equation $${\Delta}f=g-he^f$$ on an infinite graph, the prototype of which comes from the smooth Kazdan-Warner equation on an open manifold. Different from the variational methods often used in the finite graph case, we use a heat flow method to study the graph Kazdan-Warner equation. We prove the existence of a solution to the graph Kazdan-Warner equation under the assumption that $h{\leq}0$ and some other integrability conditions or constrictions about the underlying infinite graphs.