• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.839-848
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• 1998

We can obtain the concise description of two dimensional Finsler space from the viewpoint of their geodesic curves. In this paper we obtain the geodesic equations in a two-dimensional Finsler space with some special (${\alpha},\;{\beta}$)-metrics by using the Weierstrass form. We shall be referred to an isothermal coodinate system and an orthonormal one with respect to an associated Riemannian space.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.185-195
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• 2019

In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.183-200
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• 2012

In the present paper, we consider the condition that is a geodesic equation on a Finsler space with an (${\alpha},\;{\beta}$)-metric. Next we find the conditions that are equations of geodesic on the Finsler space with an approximate infinite series (${\alpha},\;{\beta}$)-metric.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.81-86
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• 2001

In this paper, we present the proof of the property for interior metric space and geodesic space.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.503-514
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• 1998

We want to treat this problem for real hypersurfaces in a complex hyperbolic space $J_n(C)$. Thus it seems to be natural to consider some problems concerned with the estimation of the Ricci tensor for real hypersurfaces in $H_n(C)$. In this paper we will find a new tensorial formula concerned with the Ricci tensor and give it a characterization of horospheres and geodesic hyperspheres in a complex hyperbolic space $H_n(C)$.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.335-341
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• 2008

In this paper, we use the convexity of distance function between geodesics in a singular Hadamard space to generalize Hadamard-Cartan theorem for 2-dimensional metric spaces. We also determine a neighborhood of a closed geodesic where no other closed geodesic exists in a complete space of nonpositive curvature.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.229-241
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• 2018

In the present study, we derive the problem of constructing a hypersurface family from a given isogeodesic curve in the 4D Galilean space $G_4$. We obtain the hypersurface as a linear combination of the Frenet frame in $G_4$ and examine the necessary and sufficient conditions for the curve as a geodesic curve. Finally, some examples related to our method are given for the sake of clarity.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.209-214
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• 1996

A flat space is characterized by tube volumes about geodesic balls. Similar characterizations are also given for other rank one symmetric spaces.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.67-74
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• 2024

Maximal surfaces have a prominent place in the field of differential geometry, captivating researchers with their intriguing properties. Bearing a direct analogy to the minimal surfaces in Euclidean space, investigating both their similarities and differences has long been an important issue. This paper is aimed to give a local characterization of maximal surfaces in 𝕃³ in terms of their geodesic curvatures, which is analogous to the minimal surface case presented in [8]. We present a classification of the maximal surfaces under some simple condition on the geodesic curvatures of the parameter curves in the line of curvature coordinates.

• 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.