• 대한수학회지
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• 제31권3호
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• pp.393-400
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• 1994

Subminifolds of Euclidean spaces have been studied by examining geodesics of the submanifolds viewed as curves of the ambient Euclidean spaces ([3], [7], [8], [9]). K.Sakamoto ([7]) studied submanifolds of Euclidean space whose geodesics are plane curves, which were called submanifolds with planar geodesics. And he completely calssified such submanifolds as either Blaschke manifolds or totally geodesic submanifolds. We now ask the following: If there is a point p of the given submanifold in Euclidean space such that every geodesic of the submanifold passing through p is a plane curve, how much can we say about the submanifold\ulcorner In the present paper, we study submanifolds of euclicean space with such property.

• Korean Journal of Mathematics
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• 제25권4호
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• pp.537-554
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• 2017

In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.441-447
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• 2002

We show that the conharmonical1y flat K-contact find cosymplectic manifolds are local1y Euclidean. Evidently non locally Euclidean conharmonically flat Sasakian manifold does not exist. Moreover we see that conharmonically flat Kenmotsu manifold does not exist and conharmonically flat fibred quasi quasi Sasakian space is locally Euclidean if and only if the scalar curvature of each fibre vanishes identically.

• 호남수학학술지
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• 제40권4호
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• pp.701-718
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• 2018

In this paper, we will study the constant mean curvature (CMC) surfaces foliated by ellipses in three dimensional Euclidean space $E^3$. We prove that: (1): Surfaces foliated by ellipses are CMC surfaces if and only if it is a part of generalized cylinder. (2): All surfaces foliated by ellipses are not minimal surfaces. (3): CMC surfaces foliated by ellipses are developable surfaces. (4): CMC surfaces foliated by ellipses are translation surfaces generated by a straight line and plane curve.

• 호남수학학술지
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• 제41권2호
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• pp.329-342
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• 2019

In this paper, we give a geometric approach to Killing magnetic flux surfaces in Euclidean 3-space and solve the differential equations which expressed the mentioned surfaces. Furthermore we give some examples and draw their pictures by using the programme Mathematica.

• Kyungpook Mathematical Journal
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• 제63권2호
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• pp.263-285
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• 2023

In this paper, we investigate the spherical indicatrices of a new relationship between Bertrand pair curves in Euclidean 3-space. We obtain necessary and sufficient conditions for this type of Bertrand pair curves to be slant helix, and provide an example.

• 대한수학회지
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• 제53권6호
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• pp.1309-1330
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• 2016

As a generalizing certain geometric property occurred on the helicoid of 3-dimensional Euclidean space regarding the Gauss map, we study ruled submanifolds in a Euclidean space with pointwise 1-type Gauss map of the first kind. In this paper, as new examples of cylindrical ruled submanifolds in Euclidean space, we construct generalized circular cylinders and characterize such ruled submanifolds and minimal ruled submanifolds of Euclidean space with pointwise 1-type Gauss map of the first kind.

• Kyungpook Mathematical Journal
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• 제28권1호
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• pp.63-69
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• 1988

In this paper we define the athwart immersions with codimension p⩾2 into Euclidean space. Some results supported by geometric examples have been established. A comparison study has been carried out throughout the paper.

• 과학교육연구지
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• 제47권3호
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• pp.263-272
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• 2023

예비교사가 비유클리드 기하학에서 수학적 정의를 이용한 이차곡선의 학습으로 유클리드 기하학의 다양한 개념을 어떻게 이해하고 활용할 수 있는지를 살펴본다. 본 연구에서는 D 대학교 수학교육과 3학년 수업에서 수학적 정의를 이용하여 택시기하, 민코프스키 거리공간과 같은 비유클리드 공간의 이차곡선 학습이 예비교사들에게 새로운 기하학적 개념을 습득하고 수용하는 능력 향상에 도움을 줄 수 있음을 보였다. 이러한 결과로부터 택시기하와 민코프스키 거리공간에서의 정의를 활용한 이차곡선 학습이 창의적이고 유연한 사고를 유도하여, 예비교사들의 유클리드 기하학 교육 전문성 향상에 기여할 것으로 기대된다.

• 호남수학학술지
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• 제45권4호
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• pp.585-597
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• 2023

We introduce the rotational hypersurface x = x(u, v, s, t) constructed by double rotation in five dimensional Euclidean space 𝔼⁵. We reveal the first and the second fundamental form matrices, Gauss map, shape operator matrix of x. Additionally, defining the i-th curvatures of any hypersurface via Cayley-Hamilton theorem, we compute the curvatures of the rotational hypersurface x. We give some relations of the mean and Gauss-Kronecker curvatures of x. In addition, we reveal Δx=𝓐x, where 𝓐 is the 5 × 5 matrix in 𝔼⁵.