• Honam Mathematical Journal
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• v.37 no.4
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• pp.457-468
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• 2015

The aim of present paper is to investigate 3-dimensional ${\xi}$-projectively flt and $\tilde{\varphi}$-projectively flt normal almost paracontact metric manifolds. As a first step, we proved that if the 3-dimensional normal almost paracontact metric manifold is ${\xi}$-projectively flt then ${\Delta}{\beta}=0$. If additionally ${\beta}$ is constant then the manifold is ${\beta}$-para-Sasakian. Later, we proved that a 3-dimensional normal almost paracontact metric manifold is $\tilde{\varphi}$-projectively flt if and only if it is an Einstein manifold for ${\alpha},{\beta}=const$. Finally, we constructed an example to illustrate the results obtained in previous sections.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1293-1307
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• 2017

General (${\alpha},{\beta}$)-metrics form a rich class of Finsler metrics. They include many important Finsler metrics, such as Randers metrics, square metrics and spherically symmetric metrics. In this paper, we find equations which are necessary and sufficient conditions for such Finsler metric to be locally projectively flat. By solving these equations, we obtain all of locally projectively flat general (${\alpha},{\beta}$)-metrics under certain condition. Finally, we manufacture explicitly new locally projectively flat Finsler metrics.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.105-114
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• 2011

In this paper, we classify (C, $\cal{L}$) such that a smooth curve C of genus g has a nonspecial very ample line bundle $\cal{L}$ of deg $\cal{L}$ = 2g-2-a failing to be normally generated, in terms of the number a.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.557-573
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• 2011

Let G be a compact and connected semisimple Lie group, H a closed subgroup, g (resp. h) the Lie algebra of G (resp. H), B the Killing form of g, g the normal metric on the homogeneous space G/H which is induced by -B. Let D be an invarint connection with Weyl structure (D, g, ${\omega}$) in the tangent bundle over the normal homogeneous Riemannian manifold (G/H, g) which is projectively flat. Then, the affine connection D on (G/H, g) is a Yang-Mills connection if and only if D is the Levi-Civita connection on (G/H, g).

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.589-607
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• 2009

In this paper we study arithmetically Cohen-Macaulay (ACM for short) vector bundles $\varepsilon$ of rank k $\geq$ 3 on hypersurfaces $X_r\;{\subset}\;{\mathbb{P}}^4$ of degree r $\geq$ 1. We consider here mainly the case of degree r = 4, which is the first unknown case in literature. Under some natural conditions for the bundle $\varepsilon$ we derive a list of possible Chern classes ($c_1$, $c_2$, $c_3$) which may arise in the cases of rank k = 3 and k = 4, when r = 4 and we give several examples.