• Bulletin of the Korean Mathematical Society
• /
• v.21 no.2
• /
• pp.61-66
• /
• 1984

It is well-known that the most interesting non-integrable almost Hermitian manifold are the nearly Kaehlerian manifolds ([2] and [3]), and that there exists a complex but not a Kaehlerian structure on Riemannian product manifolds of two normal contact manifolds [4]. The purpose of the present paper is to study nearly Kaehlerian product manifolds of two almost contact metric manifolds and investigate the geometrical structures of these manifolds. Unless otherwise stated, we shall always assume that manifolds and quantities are differentiable of class $C^{\infty}$. In Paragraph 1, we give brief discussions of almost contact metric manifolds and their Riemannian product manifolds. In paragraph 2, we investigate the perfect conditions for Riemannian product manifolds of two almost contact metric manifolds to be nearly Kaehlerian and the non-existence of a nearly Kaehlerian product manifold of contact metric manifolds. Paragraph 3 will be devoted to a proof of the following; A conformally flat compact nearly Kaehlerian product manifold of two almost contact metric manifolds is isomatric to a Riemannian product manifold of a complex projective space and a flat Kaehlerian manifold..

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

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.951-962
• /
• 2013

We introduce semi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions, etc. We obtain characterizations, investigate the integrability of distributions and the geometry of foliations, etc. We also find a condition for such submersions to be harmonic. Moreover, we give lots of examples.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1327-1340
• /
• 2019

We establish a monotonicity formula of V-harmonic maps by using the stress-energy tensor. Use the monotonicity formula, we can derive a Liouville type theorem for V-harmonic maps. As applications, we also obtain monotonicity and constancy of Weyl harmonic maps from conformal manifolds to Riemannian manifolds and ${\pm}holomorphic$ maps between almost Hermitian manifolds. Finally, a constant boundary-value problem of V-harmonic maps is considered.

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

• Proceedings of the KSR Conference
• /
• 2000.11a
• /
• pp.358-365
• /
• 2000

For the general case of loading conditions and boundary conditions, it is very difficult to obtain closed form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. In consequence, most of previous finite element formulations are introduce approximate displacement fields to use shape functions as Hermitian polynomials, and so on. The Purpose of this study is to presents a consistent derivation of exact dynamic stiffness matrices of thin-walled straight beams, to be used ill tile free vibration analysis, in which almost types of boundary conditions are exist An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element of nonsymmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequency is evaluated for the thin-walled straight beam structure, and the results are compared with analytic solutions in order to verify the accuracy of this study.

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

• Honam Mathematical Journal
• /
• v.45 no.1
• /
• pp.109-122
• /
• 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.

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