• 대한수학회논문집
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• 제23권3호
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• pp.421-426
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• 2008

Let $M^n$ be a complete immersed super stable minimal submanifold in $\mathbb{R}^{n+p}$ with fiat normal bundle. We prove that if M has finite total $L^2$ norm of its second fundamental form, then M is an affine n-plane. We also prove that any complete immersed super stable minimal submanifold with flat normal bundle has only one end.

• 대한수학회지
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• 제55권5호
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• pp.1103-1129
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• 2018

In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.

• 대한수학회보
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• 제52권1호
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• pp.301-312
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• 2015

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb{E}^4_1$.

• 대한수학회논문집
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• 제21권4호
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• pp.739-747
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• 2006

By using O(m+n, 1)/$O(m){\times}O(n,1)-system$, we give an analytic version of Ribaucour transformation for flat m-dimensional submanifolds in $\mathbb{H}^{m+n}$ with flat, non-degenerate normal bundle and free of weak umbilics, where $n{\geq}m-1$.

• 대한수학회보
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• 제31권1호
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• pp.25-33
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• 1994

In [2] we proved that if the minimum of the sectional curvature of a compact real minimal hypersurface of CP$^{m}$ is 1/(2m-1), then M is the geodesic hypersphere. This result was generalized in [8] to the case of M is a generic submanifold with flat normal connection. The purpose of the present paper is to prove a following generalization of theorems in [2] and [8].

• 호남수학학술지
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• 제33권4호
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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).

• 한국작물학회지
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• 제31권2호
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• pp.167-172
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• 1986

우리나라의 재래종 대화형 대두인 부채콩의 생육 및 형태적 특성을 정상형 대두인 단엽콩과 비교하였던 바 그 결과를 요약하면 다음과 같았다. 1. 대화형 대두인 부채콩의 주경은 생육이 진행됨에 따라 대화가 심해졌고 정상형인 단엽콩에 비해 출엽이 불규칙하였으며 주경엽수는 단엽콩보다 훨씬 증가하였으나 총엽수는 크게 다르지 않았다. 2. 부채중의 주경대화정도는 약 3.1정도였으며 대화정도는 정상형인 단엽콩의 주경과 분핵의 생육량과 유관하였다. 3. 부채콩의 분지수는 단엽콩보다 적었으나 분지가 대화하는 경우도 있었으며 엽병의 대화도 관찰되었다. 4. 부채콩은 협의 대부분이 주경 선단부에 집중 분포하였다. 5. 부채콩의 수량은 단엽콩의 60％정도였으며 수량감소의 주원인은 종실중과 협당입수의 감소였다. 6. 주경 횡단면의 유관속수는 부채콩이 많았으나 각 유관속은 단엽콩이 발달하였다.