• East Asian mathematical journal
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• 제24권4호
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• pp.421-429
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• 2008

We study invariant lightlike submanifolds and almost contact CR-lightlike submanifolds of an indefinite cosymplectic manifold.

• 대한수학회지
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• 제21권2호
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• pp.183-206
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• 1984

• 대한수학회지
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• 제37권3호
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• pp.455-461
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• 2000

The quantum hyperplane section theorem is explained for nonnegative decomposable concavex bundle spaces over generalized flag manifolds.

• 충청수학회지
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• 제24권3호
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• pp.569-581
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• 2011

Let a finite group R act smoothly on a closed manifold M. We assume that R acts freely on M except a union of closed submanifolds with codimension at least two. Then, we show that there exists an isomorphism between equivariant topological complex vector bundles over M and nonequivariant topological complex vector orbibundles over the orbifold M/R. By using this, we can classify nonequivariant vector orbibundles over the orbifold especially when the manifold is two-sphere because we have classified equivariant topological complex vector bundles over two sphere under a compact Lie group (not necessarily effective) action in [6]. This classification of orbibundles conversely explains for one of two exceptional cases of [6].

• 호남수학학술지
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• 제40권4호
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• pp.749-763
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• 2018

In this paper firstly, It was studied almost paraholomorphic vector field with respect to almost para-Nordenian structure ($F^S$, g) and the purity conditions of the Sasakian metric is investigate with respect to almost para complex structure F on cotangent bundle. Secondly, we obtained the integrability conditions of almost paracomplex structure F by calculating the Nijenhuis tensors of F of type (1, 1) on $^CT(M_n)$. Finally, the Tachibana operator ${\phi}_{\varphi}$ applied to $^Sg$ according to F and the Vishnevskii operators (${\psi}_{\varphi}$-operator) applied to the vertical and horizontal lifts with respect to F on cotangent bundle.

• 대한수학회논문집
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• 제10권4호
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• pp.949-961
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• 1995

Let f be a smooth G map from a nonsingular real algebraic G variety to an equivariant Grassmann variety. We use some G vector bundle theory to find a necessary and sufficient condition to approximate f by an entire rational G map. As an application we algebraically approximate a smooth G map between G spheres when G is an abelian group.

• 대한수학회논문집
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• 제35권3호
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• pp.1019-1035
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• 2020

In this paper, we introduce the deformed-Sasaki metric on the tangent bundle TM over an m-dimensional Riemannian manifold (M, g), as a new natural metric on TM. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the deformed-Sasaki Metric. We also construct some examples of harmonic vector fields.

• 대한수학회논문집
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• 제9권3호
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• pp.669-670
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• 1994

Let $E \to M$ be a hermitian holomorphic vector bundle over a compact (complex) hermitian manifold M of complex dimension n, and let $$ d"_p(E) : 0 \to A^{p,0}(E) \to A^{p,1}(E) \to \cdots \to A^{p,n}(E) \to 0$$ be the Dolbeault complex. Then $A^{p,q}(E)$ become a prehibert space so that the formal adjoint $\delta"$ of $d"$ and the "Laplacian" $\Delta" = \delta" d" + d" \delta"$ are defined.quot; d" + d" \delta"$ are defined.;$ are defined.

• 대한수학회보
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• 제38권1호
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• pp.157-161
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• 2001

In this paper, we prove that an affine manifold M is finitely covered by a manifold $\overline{M}$ where $\overline{M}$ is radiant or the tangent bundle of $\overline{M}$ has a conformally flat vector subbundle of the projective holonomy group of M admits an invariant probability Borel measure. This implies that$x^M$is zero.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.125-138
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• 2011

We give some characterizations of non-existence of lightlike hypersurfaces of an indefinite space form. Some geometric objects for the induced Ricci tensor to be symmetric are studied.