• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.337-346
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• 2000

The geodesic equation in a two-dimensional Finsler space is given by the differential equation of the Weierstrass form. In the present paper, we express the differential equations of geodesics in a two-dimensional Finsler space with a generalized Kropina metric.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-46
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• 2023

Geodesic orbit spaces are homogeneous Finsler spaces whose geodesics are all orbits of one-parameter subgroups of isometries. Such Finsler spaces have vanishing S-curvature and hold the Bishop-Gromov volume comparison theorem. In this paper, we obtain a complete description of invariant (α₁, α₂)-metrics on spheres with vanishing S-curvature. Also, we give a description of invariant geodesic orbit (α₁, α₂)-metrics on spheres. We mainly show that a Sp(n + 1)-invariant (α₁, α2)-metric on S⁴ⁿ⁺³ = Sp(n + 1)/Sp(n) is geodesic orbit with respect to Sp(n + 1) if and only if it is Sp(n + 1)Sp(1)-invariant. As an interesting consequence, we find infinitely many Finsler spheres with vanishing S-curvature which are not geodesic orbit spaces.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.315-336
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• 1999

In the paper [12] we have introduced the new kind of pseudo-einstein ruled real hypersurfaces in complex space forms $M_n(c), c\neq0$, which are foliated by pseudo-Einstein leaves. The purpose of this paper is to give a geometric condition for non-proper pseudo-Einstein ruled real hypersurfaces to be totally geodesic in the sense of Kimura [8] for c> and Ahn, Lee and the present author [1] for c<0.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.311-317
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• 2014

We study lightlike hypersurfaces of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of $\tilde{M}(c)$, which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodesic screen distribution.

• Journal of the Korean Data and Information Science Society
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• v.22 no.5
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• pp.961-966
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• 2011

Circular variables are those that have a period in its range. Their examples include direction of animal migration, and time of drug administration, just to mention a few. Statistical analysis of circular variables is quite different from that of linear variable due to its periodic nature. In this paper, the author proposes new circular regression models using geodesic lines on the surface of the sample space of the response and the predictor variables.

• East Asian mathematical journal
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• v.15 no.2
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• pp.337-344
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• 1999

If any geodesic on $F^n$ is also a geodesic on $\={F}^n$ and the inverse is true, the change $\sigma:L{\rightarrow}\={L}$ of the metric is called projective. In this paper, we will find the condition that a recurrent Finsler space remains to be a recurrent one under the projective change.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.395-402
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• 1999

We introduce the notion of strongly k-disk homogeneous apace and establish a characterization theorem. More specifically, we prove that any analytic Riemannian manifold (M,g) of dimension n which is strongly k-disk homogeneous with 2$\leq$k$\leq$n-1 is a space of constant curvature. Its K hler analog is obtained. The total mean curvature homogeneity of geodesic sphere in k-disk is also considered.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.655-665
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• 2021

In the present paper, we study the geometric properties of the invariant submanifold of an almost Kenmotsu structure whose Riemannian curvature tensor has (𝜅, 𝜇, 𝜈)-nullity distribution. In this connection, the necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu (𝜅, 𝜇, 𝜈)-space to be totally geodesic under the behavior of functions 𝜅, 𝜇, and 𝜈.

• 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.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.513-541
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• 2023

In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space ℝ³₁, Lorentzian sphere 𝕊²₁ and hyperbolic sphere ℍ²₀ of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in ℝ³₁ and draw the graphs of these indicatrix curves on the spheres.