• Kyungpook Mathematical Journal
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• 제54권4호
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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.

• 충청수학회지
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• 제25권1호
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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.

• 대한수학회논문집
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• 제21권2호
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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.

• 대한수학회논문집
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• 제34권2호
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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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• 제40권5_6호
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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.

• 호남수학학술지
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• 제43권4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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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.

• 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.

• Korean Journal of Mathematics
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• 제32권3호
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• pp.407-424
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• 2024

The present work aims to introduce the geometry of invariant and screen semi-invariant lightlike submanifolds of a metallic semi-Riemannian manifold equipped with a quarter symmetric non-metric connection. The study establishes the characterization of integrability and parallelism of the distributions inherent in these submanifolds. Additionally, the conditions for distributions defining totally geodesic foliations on the invariant and screen semi-invariant lightlike submanifolds of metallic semi-Riemannian manifold are specified.

• Korean Journal of Mathematics
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• 제28권2호
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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.