• 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.

• 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.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.315-333
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• 2022

We give a general procedure to analyze the structure for certain ℂ-Fuchsian subgroups of some non-arithmetic lattices. We also show their presentations and describe their fundamental domains which lie in a complex geodesic, a set homeomorphic to the unit disk.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.1
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• pp.53.2-53.2
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• 2011

A small number of active galactic nuclei are known to exhibit prominent double peak emission profiles indicating the presence of a relativistic accretion disk model. Using a Monte Carlo technique, we compute the linear polarization of a double peaked broad emission line. A Keplerian accretion disk is adopted for the double peak emission line region and the Schwarzschild geometry is assumed in the emission region. Far from the accretion disk where flat Minkowski geometry is appropriate, we place a scattering region in the shape of a spherical shell sliced. We generate a line photon in the accretion disk in an arbitraray direction in the local rest frame and follow the geodesic of the photon until it hits the scattering region. The profile of the polarized flux is mainly determined by the relative location of the scattering region with respect to the emission source. When the scattering region is in the polar direction, the linear degree of polarization also shows a double peak structure. Under a favorable condition we show that up to 1% of linear degree of polarization may be obtained.

• Journal of The Korean Astronomical Society
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• v.44 no.2
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• pp.59-65
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• 2011

A small number of active galactic nuclei are known to exhibit prominent double peak emission profiles that are well-fitted by a relativistic accretion disk model. We develop a Monte Carlo code to compute the linear polarization of a double peaked broad emission line arising from Thomson scattering. A Keplerian accretion disk is adopted for the double peak emission line region and the geometry is assumed to be Schwarzschild. Far from the accretion disk where flat Minkowski geometry is appropriate, we place an azimuthally symmetric scattering region in the shape of a spherical shell sliced with ${\Delta}{\mu}=0.1$. Adopting a Monte Carlo method we generate line photons in the accretion disk in arbitrary directions in the local rest frame and follow the geodesic paths of the photons until they hit the scattering region. The profile of the polarized flux is mainly determined by the relative location of the scattering region with respect to the emission source. When the scattering region is in the polar direction, the degree of linear polarization also shows a double peak structure. Under favorable conditions we show that up to 0.6% linear polarization may be obtained. We conclude that spectropolarimetry can be a powerful probe to reveal much information regarding the accretion disk geometry of these active galactic nuclei.