• 대한수학회지
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• 제41권5호
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• pp.795-808
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• 2004

In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension. mean curvature, sectional curvature, shape operator, k-Ricci curvature, locally conformal Kaehler space form, totally real submanifold.

• 대한수학회논문집
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• 제17권2호
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• pp.279-293
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• 2002

In this paper, we prove that if every totally real bisectional curvature of an n($\geq$3)-dimensional complete Kahler submanifold of a complex projective space of constant holomorphic sectional curvature c is greater than (equation omitted) (3n$^2$+2n-2), then it is totally geodesic and compact.

• 대한수학회보
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• 제40권1호
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• pp.63-76
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• 2003

In this article, we establish relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a slant submanifold in a Sasakian space form of constant $\varphi-sectional$ curvature with arbitrary codimension.

• 대한수학회논문집
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• 제12권1호
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• pp.87-99
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• 1997

In a 6-dimensional quasi-Kaehler manifold M with pointwise constant holomorphic sectional curvature $\mu \neq 0$, we find some conditions for M to be a space form or a complex space form.

• Korean Journal of Mathematics
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• 제13권1호
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• pp.51-59
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• 2005

Let (M, $g$) be a compact oriented self-dual 4-dimensional Einstein manifold with positive sectional curvature. Then we show that, up to rescaling and isometry, (M, $g$) is $S^4$ or $\mathbb{C}\mathbb{P}_2$, with their cannonical metrics.

• 대한수학회보
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• 제49권1호
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• pp.49-55
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• 2012

In this paper, we prove that a complex Finsler manifold is a complex locally Minkowski space if and only if it is a strictly K$\ddot{a}$hler-Berwald manifold with zero holomorphic sectional curvature.

• Kyungpook Mathematical Journal
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• 제45권2호
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• pp.231-240
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• 2005

The paper shows that a hypersurface with constant curvature with the condition $hD{\subset}D$, of a contact metric manifold with a nullity condition and ${\varphi}-constant$ sectional curvature, has the curvature equals to k and ${\mu}=0$.

• 대한수학회지
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• 제61권1호
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• pp.183-205
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• 2024

In this paper, for an m-dimensional (m ≥ 5) complete non-compact submanifold M immersed in an n-dimensional (n ≥ 6) simply connected Riemannian manifold N with negative sectional curvature, under suitable constraints on the squared norm of the second fundamental form of M, the norm of its weighted mean curvature vector |H_f| and the weighted real-valued function f, we can obtain: • several one-end theorems for M; • two Liouville theorems for harmonic maps from M to complete Riemannian manifolds with nonpositive sectional curvature.

• Korean Journal of Mathematics
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• 제13권1호
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• pp.35-41
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• 2005

Let (M, $g$) be a compact oriented 4-dimensional Riemannian manifold whose sectional curvature $k$ satisfies $1{\geq}k{\geq}0.1714$. We show that M is topologically $S^4$ or ${\pm}\mathbb{C}\mathbb{P}^2$.

• 대한수학회보
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• 제50권1호
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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 $S^4$.