• Bulletin of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.741-755
• /
• 1998

We prove the asymptotic lens equivalence in manifolds without conjugate points. By using this property we show that under a metric condition of asymptotically Euclidean and the curvature condition decaying faster than quadratic, any surface $(R^2,g)$ without conjugate points is Euclidean.

• 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 Chungcheong Mathematical Society
• /
• v.30 no.4
• /
• pp.369-379
• /
• 2017

In this paper, we shall study the existence and distribution of conjugate points in Finsler geometry from the viewpoint of the oscillation and Morse index theory.

• Communications of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.1025-1039
• /
• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.285-292
• /
• 2001

The authors compute the Ricci curvature of the GRW space-time to obtain two conditions for the conjugate points which appear as the Timelike Convergence Condition(TCG) and the Jacobi inequality. Moreover, under such two conditions, we obtain a lower bound of the length of a unit timelike geodesic for focal points emanating form the immersed spacelike hypersurface, the graph over the fiber in the GRW space-time.

• Journal of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.61-72
• /
• 2003

Let N be the quaternionic Heisenberg group equipped with a left-invariant metric. We characterize all the conjugate points along the geodesics on N.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.28 no.4
• /
• pp.463-469
• /
• 2010

Since MOLA(Mars Orbiter Laser Altimeter) data, which provides altimetry data for Mars, does not cover the whole Mars area, image matching with MOC imagery should be implemented for the generation of DEM. However, automatic image matching is difficult because of insufficient features and low contrast. In this paper, we present the area based semi-automatic image matching algorithm with MOC-NA(Mars Orbiter Camera ? Narrow Angle) imagery. To accomplish this, seed points describing conjugate points are manually added for the stereo imagery, and interesting points are automatically produced by using such seed points. Produced interesting points being used as initial conjugate points, area based image matching is implemented. For the points which fail to match, the locations of initial conjugate points are recalculated by using matched six points and image matching process is re-implemented. The quality assessment by reversing the role of target and search image shows 97.5 % of points were laid within one pixel absolute difference.

• Korean Journal of Mathematics
• /
• v.24 no.3
• /
• pp.397-407
• /
• 2016

In this paper, the concepts of k-smoothness, k-very smoothness and k-strongly smoothness of Banach spaces are dealt with together briefly by introducing three types k-denting point regarding different topology of conjugate spaces of Banach spaces. In addition, the characterization of first type ${\omega}^*-k$ denting point is described by using the slice of closed unit ball of conjugate spaces.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.18 no.3
• /
• pp.315-322
• /
• 2000

DSM(Digital Surface Model) is a digital model which represents the surface elevation of a region. DSM is necessary for orthoimage generation, and frequently used in man-made object extraction from aerial photographs nowadays. Image matching technique enables automatic DSM generation. This proposed a image matching method which can be applied to automatic generation of DSM for Built-up Area. The matching method proposed is to find conjugate points and conjugate lines from overlapping aerial images. In detecting conjugate points, the positional relation between possible conjugate point pair as well as correlation of pixel gray value is compared. In detecting conjugate lines, the color attribute of flank region of line, shape of line, positional relation between neighborhood points and lines, and the connection relation between lines are compared. The proposed matching method is assumed to be useful for DSM generation including Built-up Area.