• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.917-926
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• 1994

Let ($M, G_M, F$) be a (p+q)-dimensional Riemannian manifold with a foliation F of codimension q and a bundle-like metric $g_M$ with respect to F ([9]). Aside from the Laplacian $\bigtriangleup_g$ associated to the metric g, there is another differnetial operator, the Jacobi operator $J_D$, which is a second order elliptic operator acting on sections of the normal bundle. Its spectrum isdiscrete as a consequence of the compactness of M. The study of the spectrum of $\bigtriangleup_g$ acting on functions or forms has attracted a lot of attention. In this point of view, the present authors [7] have studied the spectrum of the Laplacian and the curvature of a compact orientable cosymplectic manifold. On the other hand, S. Nishikawa, Ph. Tondeur and L. Vanhecke [6] studied the spectral geometry for Riemannian foliations. The purpose of the present paper is to study the relation between two spectra and the transversal geometry of cosymplectic foliations. We shall be in $C^\infty$-category. Manifolds are assumed to be connected.

• Journal of Energy Engineering
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• v.12 no.4
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• pp.253-258
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• 2003

Manual type manifold gauge has been used for charging the refrigerant in the refrigeration systems. In this case, the refrigerant is released to the ambient during the hose-switching period. :he objectives of this study are to develop a novel automatic refrigerant charging system, and to quantify the effect of the automatic systems on the reduction of the non-condensable gas and the contamination of the compressor oil. The automatic charging system makes the pressure test, vacuum test, and refrigerant charging work very simple and easy because the charging hose does not have to be switched many times. It is found that the amount of water in the SiO$_2$and the compressor oil reduces to l/4 times of that for the manual type manifold gauge and the refrigerant is not released to the ambient at all when the automatic charging system is adopted.

• Journal of Biosystems Engineering
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• v.8 no.1
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• pp.38-46
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• 1983

This study was carried out to investigate the possibility of improving the performance of a kerosene engine with water addition. The engine used in this study was a single-cylinder, four-cycle kerosene engine with the compression ratio of 4.5. Water could be successfully added into the inlet manifold by an extra carburetor for the volumetric ratios of 5, 10, 20, and 30 percents. Variable speed tests at wide-open throttle were performed for five speed levels in the range of 1,000 to 2,200rpm for each fuel type. Volumetric efficiency and brake specific fuel consumption were determined, and brake thermal efficiency based on the lower heats of combustion of kerosene was calculated. To examine variation in fuel consumption, CO concentration, and cooling water temperature, part load tests were also performed. The results obtained are summarized as follow. (1) Brake torque increased almost in proportion to volumetric efficiency. But the ratio of increase in torque was greater than that of volumetric efficiency. Mean torque over the speed range of 1,000 to 2,200rpm increased 1, 3, 7, and 2 percents for 5, 10, 20, and 30 percents water addition, respectively. The increase in brake torque with water addition was greater at lower speeds. (2) Mean brake specific fuel consumption over the speed range of 1,000 to 2,200rpm decreased 1, 2, 3, and 3 percents for 5, 10, 20, and 30 percents water addition, respectively. (3) Mean temperature of cooling water over the speed range of 1,000 to 2,200rpm decreased 2, 4, 8, and 12 percents for 5, 10, 20, and 30 percents water addition, respectively. (4) The effects of decreasing CO concentration in the exhaust emissions with water addition were significant. At the speed range of 1,000 to 2,200rpm, CO concentration in the exhaust emissions decreased 2, 10, 23, percents for 5, 10, and 20 percents water addition, respectively. (5) Deposits were not discovered in the combustion chamber during the experiment. However, a little rust was formed in the water-supply carburetor.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.135-142
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• 2013

In the present paper, we discuss the rigidity phenomenon of closed minimal submanifolds in a locally symmetric Riemannian manifold with pinched sectional curvature. We show that if the sectional curvature of the submanifold is no less than an explicitly given constant, then either the submanifold is totally geodesic, or the ambient space is a sphere and the submanifold is isometric to a product of two spheres or the Veronese surface in $S^4$.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1065-1087
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• 1997

We prove that there exists a canonical level-preserving isomorphism between the stable Morse homology (or the Morse homology of generating functions) and the Floer homology on the cotangent bundle $T^*M$ for any closed submanifold $N \subset M$ for any compact manifold M.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.701-706
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• 1999

A characterization of geodesic spheres in the simply connected space forms in terms of the ratio of the Gauss-Kronecker curvature and the (usual) mean curvature is given: An immersion of n dimensional compact oriented manifold without boundary into the n + 1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilicimmersion if the mean curvature $H_1$ does not vanish and the ratio $H_n$/$H_1$ of the Gauss-Kronecker curvature $H_n$ and $H_1$ is constant.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.83-90
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• 2016

We show that any orthogonal almost complex structure on a warped product Riemannian manifold of an oriented closed surface with nonnegative Gaussian curvature and a round 4-sphere is never integrable. This provides a partial answer to a question raised by E. Calabi.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1273-1283
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• 2018

Let ($M,{\mathcal{F}}$) be a closed, oriented Riemannian manifold of a foliation ${\mathcal{F}}$ with a nonisometric transversal conformal field. Then ($M,{\mathcal{F}}$) is transversally isometric to the sphere under some transversal concircular curvature conditions.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1927-1933
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• 2017

We prove that there are rational homology balls $B_p$ smoothly embedded in the 2-handlebodies associated to certain knots. Furthermore we show that, if we rationally blow up the 2-handlebody along the embedded rational homology ball $B_p$, then the resulting 4-manifold cannot be obtained just by a sequence of ordinary blow ups from the 2-handlebody under a certain mild condition.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.387-394
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• 2010

In this paper, we study the generalized Randers change $^*L(x,y)=L(x,y)+b_i(x,y)y^i$ from the Brewald metric L and the h-vector $b_i$. And in search for a non-Berwald Landsberg metric, we obtain the conditions on $b_i(x,y)$ under which $^*L$ is a Landsberg metric.