• Journal of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.393-400
• /
• 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.

• Honam Mathematical Journal
• /
• v.40 no.4
• /
• pp.701-718
• /
• 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.

• Kyungpook Mathematical Journal
• /
• v.63 no.2
• /
• pp.263-285
• /
• 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.

• Korean Journal of Mathematics
• /
• v.25 no.4
• /
• pp.537-554
• /
• 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.

• Honam Mathematical Journal
• /
• v.41 no.2
• /
• pp.329-342
• /
• 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.

• Honam Mathematical Journal
• /
• v.36 no.1
• /
• pp.113-129
• /
• 2014

In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space $\mathbb{E}_3$ also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

• Journal of Science Education
• /
• v.47 no.3
• /
• pp.263-272
• /
• 2023

We consider how a pre-service teacher can understand and utilize various concepts of Euclidean geometry by learning conic sections using mathematical definitions in non-Euclidean geometry. In a third-grade class of D University, we used mathematical definitions to demonstrate that learning conic sections in non-Euclidean space, such as taxicab geometry and Minkowski distance space, can aid pre-service teachers by enhancing their ability to acquire and accept new geometric concepts. As a result, learning conic sections using mathematical definitions in taxicab geometry and Minkowski distance space is expected to contribute to enhancing the education of pre-service teachers for Euclidean geometry expertise by fostering creative and flexible thinking.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.637-644
• /
• 2008

In this paper, we study some properties about the parallel surfaces of ruled surfaces in a Euclidean 3-space. Furthermore, we classify the parallel surfaces of ruled surfaces in a Euclidean 3-space satisfying a linear type and a quadric type with respect to the Gaussian curvature and the mean curvature.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.359-366
• /
• 2009

In this paper, we study a tube in a Euclidean 3-space satisfying some equation in terms of the Gaussian curvature, the mean curvature and the second Gaussian curvature.

• Journal of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1309-1330
• /
• 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.