• Honam Mathematical Journal
• /
• v.40 no.1
• /
• pp.187-198
• /
• 2018

In this paper, we study the instantaneous geometric properties of motion of rigid bodies in the Lorentzian plane. For this purpose we define Lorentzian form of Bottemas instantaneous invariants. In these regards, we obtain the necessary and sufficient condition of a Lorentzian plane to be at Cardan position with respect to these invariants.

• Journal of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.455-468
• /
• 1996

Certain analytic behavior of geometric objects defined on a Riemannian manifold depends on some very crude properties of the manifold. Some of those crude invariants are the volume growth rate, isoperimetric constants, and the likes. However, these crude invariants sometimes exercise surprising control over the analytic behavior.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.1095-1103
• /
• 2016

B. Y. Chen introduced a series of curvature invariants, known as Chen invariants, and proved sharp estimates for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature, for submanifolds in Riemannian space forms. Special classes of submanifolds in Sasakian manifolds play an important role in contact geometry. F. Defever, I. Mihai and L. Verstraelen [8] established Chen first inequality for C-totally real submanifolds in Sasakian space forms. Also, the differential geometry of slant submanifolds has shown an increasing development since B. Y. Chen defined slant submanifolds in complex manifolds as a generalization of both holomorphic and totally real submanifolds. The slant submanifolds of an almost contact metric manifolds were defined and studied by A. Lotta, J. L. Cabrerizo et al. A Chen first inequality for slant submanifolds in Sasakian space forms was established by A. Carriazo [4]. In this article, we improve this Chen first inequality for special contact slant submanifolds in Sasakian space forms.

• Communications of the Korean Mathematical Society
• /
• v.8 no.4
• /
• pp.699-707
• /
• 1993

• Journal of Educational Research in Mathematics
• /
• v.24 no.4
• /
• pp.515-536
• /
• 2014

In the present study, we analyze four seventh grade students' recognition of geometric properties and the following justification processes while their adopting different construction approaches in GSP(Geometer's Sketchpad). As the students recognized dependency and level-1 invariants by dragging activities, they determined their own construction approaches. Two students, who preferred robust construction, immediately recognized the path of a draggable point and provided step-1 justification. The other students attempted soft construction followed by their recognition of level-2 invariants and the path, and came to step-2 justification.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.2071-2093
• /
• 2015

In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of ${\mathbb{E}}_1^n$. We determine the parametrizations of non-null self-similar curves in ${\mathbb{E}}_1^n$.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1101-1114
• /
• 1996

In Riemannian geometry, it is one of the important things to study the topological or geometric invariants of manifolds since they characterize the topology of manifolds.

• Communications of the Korean Mathematical Society
• /
• v.18 no.1
• /
• pp.87-94
• /
• 2003

We use geometric properties of Gromov-Hausdorff-convergence to present a way to construct rough but natural invariants of metric geometry.

• Journal of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.137-144
• /
• 1996

One of the fundamental problems in Riemannian geometry is "How the geometric invariants of Riemannian manifolds influenced by the curvature restriction \ulcorner".ner".uot;.

• Communications of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.147-163
• /
• 2017

We define de Sitter focal surfaces and hyperbolic focal surfaces of hyperbolic space curves. As an application of the theory of unfoldings of function germs, we investigate the singularities of these surfaces. For characterizing the singularities of these surfaces, we discover a new hyperbolic invariants and investigate the geometric meanings.