• The Pure and Applied Mathematics
• /
• v.11 no.3
• /
• pp.197-206
• /
• 2004

We obtain some characterizations of a pseudo Ricci-parallel real hypersurface in a quaternionic projective space $QP^{n}$ and find the condition that M is locally congruent to a geodesic hypersphere of $QP^{n}$ .

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.327-335
• /
• 2005

For a compact and orientable minimal real hypersurface $M\;in\;QP^n$, we prove that if the minimum of the sectional curvatures of Mis 3/(4n - 1), then M is isometric to the geodesic minimal hypersphere $M_{0,n-1}^Q$.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.769-781
• /
• 2011

We study the geometry of half lightlike sbmanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric metric connection subject to the conditions: (1) The screen distribution S(TM) is totally umbilical (geodesic) and (2) the co-screen distribution $S(TM^{\bot})$ of M is a conformal Killing one.

• Journal of Korean Association for Spatial Structures
• /
• v.23 no.4
• /
• pp.27-34
• /
• 2023

In this study, the seismic response characteristics of the three analysis model with or without TMD were investigated to find out the effective dome shape. The three analysis models are rib type, lattice type and geodesic type dome structure composed of space frame. The maximum vertical and horizontal displacements were evaluated at 1/4 point of the span by applying the resonance harmonic load and historical earthquake loads (El Centro, Kobe, Northridge earthquakes). The study of the effective TMD installation position for the dome structure shows that seismic response control was effective when eight TMDs were installed in all types of analysis model. The investigation of the efficiency of TMD according to dome shape presents that lattice dome and geodesic dome show excellent control performance, while rib dome shows different control performance depending on the historical seismic loads. Therefore, lattice and geodesic types are desirable for seismic response reduction using TMD compared to rib type.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.549-570
• /
• 2022

In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.

• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.195-200
• /
• 2010

Let C be a closed convex set in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$. Assume that ${\Sigma}$ is an n-dimensional compact minimal submanifold outside C such that ${\Sigma}$ is orthogonal to ${\partial}C$ along ${\partial}{\Sigma}{\cap}{\partial}C$ and ${\partial}{\Sigma}$ lies on a geodesic sphere centered at a fixed point $p{\in}{\partial}{\Sigma}{\cap}{\partial}C$ and that r is the distance in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$ from p. We make use of a modified volume $M_p({\Sigma})$ of ${\Sigma}$ and obtain a sharp relative isoperimetric inequality $$\frac{1}{2}n^n{\omega}_nM_p({\Sigma})^{n-1}{\leq}Vol({\partial}{\Sigma}{\sim}{\partial}C)^n$$, where ${\omega}_n$ is the volume of a unit ball in ${\mathbb{R}}^n$ Equality holds if and only if ${\Sigma}$ is a totally geodesic half ball centered at p.

• Honam Mathematical Journal
• /
• v.46 no.2
• /
• pp.279-290
• /
• 2024

In this study, tubular surfaces were introduced according to the modified orthogonal frame defined at the points where the torsion is different from zero in the 3-dimensional Euclidean space. First, the relations between the Frenet frame and the modified orthogonal frame with torsion are given. Then, the singularity, Gaussian curvature, mean curvature and basic forms of the tubular surface given according to the modified orthogonal frame with torsion were calculated. In addition, the conditions for the parameter curves of the tubular surface to be geodesic, asymptotic and line of curvature were examined. Finally, tubular surface examples based on both the Frenet frame and the modified orthogonal frame with torsion were given to support the study.

• The Pure and Applied Mathematics
• /
• v.19 no.1
• /
• pp.1-5
• /
• 2012

We study surfaces of revolution in the three dimensional Euclidean space $\mathbb{R}^3$ with two distinct axes of revolution. As a result, we prove that if a connected surface in the three dimensional Euclidean space $\mathbb{R}^3$ admits two distinct axes of revolution, then it is either a sphere or a plane.

• Journal of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.321-336
• /
• 1997

Let S be the Ricci curvature of an n-dimensional compact minimal totally real submanifold M of a quaternion projective space $HP^n (c)$ of quaternion sectional curvature c. We proved that if $S \leq \frac{16}{3(n -2)}c$, then either $S \equiv \frac{4}{n - 1}c$ (i.e. M is totally geodesic or $S \equiv \frac{16}{3(n - 2)}c$. All compact minimal totally real submanifolds of $HP^n (c)$ satisfy in $S \equiv \frac{16}{3(n - 2)}c$ are determined.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.1375-1397
• /
• 2014

In this paper we establish codimension reduction theorem for submanifolds of a (4m+3)-dimensional unit sphere $S^{4m+3}$ with Sasakian 3-structure and apply it to submanifolds of a quaternionic projective space.