• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.1015-1029
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• 2003

In this paper, we study a connected, simply connected homogeneous Kahler surface with distinct constant Ricci eigenvalues, and specify the local structure of them.

• Honam Mathematical Journal
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• v.45 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.457-464
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• 2003

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.629-647
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• 2023

We introduce the study of a new class of a lightlike submersion d. Then, we derive a relationship between the holomorphic section 𝜙 : K₁ → K' from a screen generic lightlike submanifold of an indefinite Kaehler manifold K₂ onto an indefinite almost Hermitian manifold K', and show that for this case K' must be an indefinite Kaehler manifold. Then, we derive a relationship between the holomorphic sectional curvatures of K₂ and K'. Finally, we present a classification theorem for a screen generic lightlike submersion, giving the relationship between the sectional curvatures of the total space K₂ and the fibers.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.795-809
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• 2020

In the present paper, we introduce the notion of quasi hemi-slant submanifolds of almost Hermitian manifolds and give some of its examples. We obtain the necessary and sufficient conditions for the distributions to be integrable. We also investigate the necessary and sufficient conditions for these submanifolds to be totally geodesic and study the geometry of foliations determined by the distributions. Finally, we obtain the necessary and sufficient condition for a quasi hemi-slant submanifold to be local product of Riemannian manifold.