• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.97-104
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• 2023

In the present paper, we characterize, for a class of almost Kenmotsu manifolds, those that admit quasi Yamabe solitons. We show that if a (k, 𝜇)'-almost Kenmotsu manifold admits a quasi Yamabe soliton (g, V, 𝜆, 𝛼) where V is pointwise collinear with 𝜉, then (1) V is a constant multiple of 𝜉, (2) V is a strict infinitesimal contact transformation, and (3) (£_Vh')X = 0 holds for any vector field X. We present an illustrative example to support the result.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1101-1110
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• 2005

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.109-122
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• 2003

In this paper we give a characterization of an irreducible connection with harmonic curvature over a connected Kaehler manifold to be self-dual. Also we introduce new notions of $c_{i}-self-dual$ or Kaehler Yang-Mills connections on compact Kaehler manifolds and investigate some fundamental properties of this kind of new connections. Moreover, on a compact odd dimensional Riemannian manifold we give a property of generalized monopole.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.163-176
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• 2016

The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, ${\mu}$)-contact metric manifolds.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.471-482
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• 1995

A complex n-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a comples space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form consists of a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. The induced almost contact metric structure of a real hypersurface M of $M_n(c)$ is denoted by $(\phi, \zeta, \eta, g)$.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.1097-1104
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• 2015

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a lightlike hypersurface M subject such that the almost contact structure vector field ${\zeta}$ of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. We prove a classification theorem of such an indefinite generalized Sasakian space form.

• 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.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.675-689
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• 2010

For a closed symplectic 4-manifold X, let $Diff_0$(X) be the group of diffeomorphisms of X smoothly isotopic to the identity, and let Symp(X) be the subgroup of $Diff_0$(X) consisting of symplectic automorphisms. In this paper we show that for any finitely given collection of positive integers {$n_1$, $n_2$, $\ldots$, $n_k$} and any non-negative integer m, there exists a closed symplectic (or K$\ddot{a}$hler) 4-manifold X with $b_2^+$ (X) > m such that the homologies $H_i$ of the quotient space $Diff_0$(X)/Symp(X) over the rational coefficients are non-trivial for all odd degrees i = $2n_1$ - 1, $\ldots$, $2n_k$ - 1. The basic idea of this paper is to use the local invariants for symplectic 4-manifolds with contact boundary, which are extended from the invariants of Kronheimer for closed symplectic 4-manifolds, as well as the symplectic compactifications of Stein surfaces of Lisca and Mati$\acute{c}$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1715-1723
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• 2016

We study the characteristic Jacobi operator ${\ell}={\bar{R}({\cdot},{\xi}){\xi}$ (along the Reeb flow ${\xi}$) on the unit tangent sphere bundle $T_1M$ over a Riemannian manifold ($M^n$, g). We prove that if ${\ell}$ is pseudo-parallel, i.e., ${\bar{R}{\cdot}{\ell}=L{\mathcal{Q}}({\bar{g}},{\ell})$, by a non-positive function L, then M is locally flat. Moreover, when L is a constant and $n{\neq}16$, M is of constant curvature 0 or 1.

• Journal of the Korean Institute of Telematics and Electronics
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• v.17 no.5
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• pp.15-21
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• 1980

An engine control system in which the conventional mechanical ignition system is studied. The contact point of the breaker is replaced by the contactless magnetic pick up sensor from which the information of the speed and the position of the crankshaft is extracted , and further an electronic High Energy Ignitim System Is designed, implemented and tested . The High Energy Igniticwl System increases the secondary spark voltage of the ignition coil from the conventional 10000~15000 volts to the 30000~40000 volts resulting in improving the combustion efficiency. Also, instead of the conventional advimce mechanism forigniliontiming control, a microprocessorbased timinng mechanisn is installed to determine the ignition timing data in response to the engine rpm and the intake manifold vacuum.