• 대한수학회보
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• 제34권4호
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• pp.653-665
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• 1997

We define an almost quaternionic Kaehler product manifold and study its submanifolds. Moreover we construct the curvature tensor of the product manifold of two quaternionic forms.

• 대한수학회보
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• 제55권2호
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• pp.515-531
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• 2018

Jin studied lightlike hypersurfaces of an indefinite Kaehler manifold [6, 8] or indefinite trans-Sasakian manifold [7] with a quarter-symmetric metric connection. Jin also studied generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection [10]. We study generic lightlike submanifolds of an indefinite Kaehler manifold with a quarter-symmetric metric connection.

• 호남수학학술지
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• 제44권3호
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• pp.432-446
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• 2022

This article introduces the structure of GCR-lightlike submanifolds of an indefinite Kaehler statistical manifold and derives their geometric properties. The characterizations on totally geodesic, mixed geodesic, D-geodesic and D'-geodesic GCR-lightlike submanifolds have also been obtained.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.133-141
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• 2009

We study on semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds. We prove that a (2n + 1)-dimensional Sasakian hypersurface M of a (2n+2)-dimensional Kaehler manifold $\widetilde{M}^{2n+2}$ is semiparallel if and only if it is totally umbilical with unit mean curvature, if dimM = 3 and $\widetilde{M}^4$ is a Calabi-Yau manifold, then $\widetilde{M}$ is flat at each point of M. We also prove that such a hypersurface M is Weyl-semiparallel if and only if it is either an ${\eta}$-Einstein manifold or semiparallel. We also investigate the extended classes of semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds.

• 대한수학회논문집
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• 제35권3호
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• pp.979-998
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• 2020

We study totally umbilical real half lightlike submanifolds of indefinite Kaehler manifolds with a quarter-symmetric metric connection. We obtain some conditions for a real half lightlike submanifold of an indefinite Kaehler manifold with a quarter-symmetric metric connection to be a product manifold. We derive the expression for induced Ricci type tensor 𝓡^(0,2) and also obtain conditions for 𝓡^(0,2) to be symmetric.

• 대한수학회논문집
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• 제12권1호
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• pp.87-99
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• 1997

In a 6-dimensional quasi-Kaehler manifold M with pointwise constant holomorphic sectional curvature $\mu \neq 0$, we find some conditions for M to be a space form or a complex space form.

• East Asian mathematical journal
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• 제30권5호
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• pp.599-607
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• 2014

We study lightlike hypersurfaces M of an indefinite Kaehler manifold $\bar{M}$ of quasi-constant curvature subject to the condition that the curvature vector field of $\bar{M}$ belongs to the screen distribution S(TM). We provide several new results on such lightlike hypersurfaces M.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.329-334
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• 2000

In this paper, we get staled harmonic maps of an almost Kaehler manifold into itself, using the stability theorem.

• 대한수학회논문집
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• 제32권1호
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• pp.119-133
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• 2017

In this paper, we study half lightlike submanifolds of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. First, we characterize the geometry of two types of half lightlike submanifolds of such an indefinite Kaehler manifold. Next, we investigate the geometry of half lightlike submanifolds of an indefinite complex space form with a semi-symmetric non-metric connection.

• 대한수학회지
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• 제54권1호
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• pp.101-115
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• 2017

In this paper, we study three types of lightlike hypersurfaces, which are called recurrent, Lie recurrent and Hopf lightlike hypersurfaces, of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. We provide several new results on such three types of lightlike hypersurfaces of an indefinite Kaehler manifold or an indefinite complex space form, with a semi-symmetric non-metric connection.