• East Asian mathematical journal
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• v.39 no.1
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• pp.37-42
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• 2023

The purpose of this paper is to establish the notion of semi-Riemannian manifolds M with the homogeneous geodesics, and investigate properties about certain homogeneity.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1011-1018
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• 2022

In this work, magnetic geodesics over the space of Kähler potentials are studied through a variational method for a generalized Landau-Hall functional. The magnetic geodesic equation is calculated in this setting and its relation to a perturbed complex Monge-Ampère equation is given. Lastly, the magnetic geodesic equation is considered over the special case of toric Kähler potentials over toric Kähler manifolds.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.83-108
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• 2023

We find geodesics on a surface numerically by using Runge-Kutta method with Python.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.577-585
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• 2008

In this paper, we shall calculate the volume of normal tubes around geodesics under a curvature perturbation to establish a theorem of volume comparison type.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.5.2-5
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• 2003

In this paper, we are to find the condition that a two-dimensional Finsler space with Matsumoto metric satisfying L(${\alpha}$,${\beta}$)=${\alpha}$$^2$/(${\alpha}$-${\beta}$) be a Landsberg space and the differential equations of geodesics.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.291-297
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• 2006

We find unit Killing vectors and homogeneous geodesics on the Lie group with Lie algebra $\mathbf{a}{\oplus}_p\mathbf{r}$, where $\mathbf{a}$ and $\mathbf{r}$ are abelian Lie algebra of dimension n and 1, respectively.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.189-193
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• 1998

In this paper we construct a sequence of spaces which has Gromov-Hausdorff limit such that a geodesic in the limit space is not realized as a limit of geodesics in the spaces of the sequence. This contrasts with the result of Grove and Petersen in [1] where they proved otherwise for Alexandrov spaces with common curvature bounds.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1335-1349
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• 2020

In this paper, we give an equivalent characterization for general (α, β)-metrics with reversible geodesics when the dimension of the manifold is greater than 2.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.233-236
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• 1992

Let f:M.rarw.N be a smooth map between Rioemannian manifolds M and N. If f maps geodesics of M to geodesics of N, f is called totally geodesic. As is well known, totally geodesic maps are harmonic and the image f(M) of a totally geodesic map f:M.rarw. N is an immersed totally geodesic submanifold of N (cf. .cint. 6.3 of [W]). We are interested in the following question: When is a harmonic map f:M .rarw. N with rank .leq. 1 everywhere on M totally geodesic\ulcorner In other words, when is the image of a harmonic map f:M .rarw. N with rank .leq. 1 everywhere on M geodesics of N\ulcorner In this note, we give some sufficient conditions on curvatures of M. It is interesting that no curvature assumptions on target manifolds are necessary in Theorems 1 and 2. Some properties of totally geodesic maps are also given in Theorem 3. We think our Theorem 3 is somewhat unusual in view of the following classical theorem of Eells and Sampson (see pp.124 of [ES]).