• Bulletin of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.25-32
• /
• 1998

Let N be the 3-dimensional Heisenberg group equipped with a left-invariant metric on N. We characterize the Jacobi fields and the conjegate points along a geodesic on N, which points out that Theorem 4 of [1] is not correct.

• Journal of the Chungcheong Mathematical Society
• /
• v.11 no.1
• /
• pp.143-150
• /
• 1998

In this paper, we investigate some properties of Jacobi fields and conjugate points in a complete Riemannian manifold M. Also we get a necessary and sufficient condition about a geodesic without conjugate points in the manifold with non-negative curvature.

• Journal of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.725-736
• /
• 1999

In the present paper we will give a characterization of homogeneous real hypersurfaces of type A1, A2 and B of a complex projective space.

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

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.4
• /
• pp.363-368
• /
• 2018

The aim of this work is to derive a partial differential equation that explains the movement of vortex lines on a vortex trajectory surface in a three dimensional incompressible inviscid flow.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.2
• /
• pp.197-203
• /
• 2020

We prove that any simple Finsler manifolds with the same distances between points of the boundary have the same Holmes-Thompson volume.

• Honam Mathematical Journal
• /
• v.40 no.3
• /
• pp.521-528
• /
• 2018

The object of the present paper is to study a decomposable $(APS)_n$ and hypersurfaces of $(APS)_n$. Also, the existence of a decomposable $(APS)_n$ is ensured by a proper example.

• Communications of the Korean Mathematical Society
• /
• v.30 no.4
• /
• pp.481-491
• /
• 2015

We calculate volume ratio of a hypersurface orthogonal to a timelike geodesic relative to that of a hypersurface in the FLRW space-time.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.11-24
• /
• 2012

We characterize the class of inner uniform domains in terms of the quasihyperbolic metric and the quasihyperbolic geodesic. We also characterize uniform domains and inner uniform domains in terms of weak Bloch functions.

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