• 대한수학회논문집
• /
• 제18권1호
• /
• 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.

• 한국정보과학회논문지:시스템및이론
• /
• 제31권5_6호
• /
• pp.288-296
• /
• 2004

본 논문은 미분오차 척도를 이용하여 메쉬를 간략화 하는 새로울 알고리즘을 제안한다. 많은 간략화 알고리즘은 거리 오차 척도를 이용하였으나, 거리 오차 척도는 높은 곡률을 갖는 동시에 작은 거리오차를 갖는 지역에 대해서는 메쉬 간략화를 위한 정확한 기하학적 오차 측정이 어렵다. 본 논문은 간략화를 위해 새로운 오차 척도인 미분 오차 척도를 제안한다. 미분 오차 척도란 거리 오차 척도와 거리 오차의 1차 미분인 탄젠트 오차 척도, 그리고 거리 오차의 2차 미분인 곡률 오차 척도를 합하여 정의된 오차척도로서, 모델의 특징 부분의 형상을 최대한으로 보존 가능하다. 메쉬는 이산 표면이지만 알지 못하는 부드러운 표면의 불연속선형 근사로 표현될 수 있고, 이산 표면은 미분이 추정 가능하므로 미분 오차 척도라는 새로운 개념을 도입할 수 있다. 본 간략화 알고리즘은 반복적인 모서리 축약(Edge Collapse)에 바탕을 두고 있고, 미분 오차 척도를 이용하여 기하학적으로 원래의 형상이 잘 유지되는 새로운 점의 위치를 찾을 수 있다. 본 논문에서는 기존 방법보다 더 작은 기하학적인 오차와 높은 품질의 간략화 된 모델의 예를 보여준다.

• Journal of applied mathematics & informatics
• /
• 제41권1호
• /
• pp.193-203
• /
• 2023

In view of solution to the Hilbert fourth problem, the present study engages to investigate the projectively flat special (𝛼, 𝛽)-metric and the generalised first approximate Matsumoto (𝛼, 𝛽)-metric, where 𝛼 is a Riemannian metric and 𝛽 is a differential one-form. Further, we concluded that 𝛼 is locally Projectively flat and have 𝛽 is parallel with respect to 𝛼 for both the metrics. Also, we obtained necessary and sufficient conditions for the aforementioned metrics to be locally projectively flat.

• 대한수학회지
• /
• 제57권6호
• /
• pp.1335-1345
• /
• 2020

We will show a rigidity of a Kähler potential of the Poincaré metric with a constant length differential.

• Nonlinear Functional Analysis and Applications
• /
• 제27권3호
• /
• pp.663-677
• /
• 2022

This present paper extends some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Kannan type mappings. Non-trivial examples are further provided to support the hypotheses of our results.

• 대한수학회보
• /
• 제28권2호
• /
• pp.231-241
• /
• 1991

Recently, many mathematicians([NT], [Ka], [TV], [CW], etc.) studied foliated structures on a smooth manifold with the viewpoint of transversal differential geometry. In this paper, we shall discuss certain hermitian foliations F on a riemannian manifold with a bundle-like metric, that is, their transversal bundles to F have hermitian structures.

• 대한수학회보
• /
• 제61권3호
• /
• pp.849-866
• /
• 2024

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

• 대한수학회보
• /
• 제26권1호
• /
• pp.47-52
• /
• 1989

Methods of Riemannian geometry has played an important role in the study of compact transformation groups. Every effective action of a compact Lie group on a differential manifold leaves a Riemannian metric invariant and the study of such actions reduces to the one involving the group of isometries of a Riemannian metric on the manifold which is, a priori, a Lie group under the compact open topology. Once an action of a compact Lie group is given an invariant metric is easily constructed by the averaging method and the Lie group is naturally imbedded in the group of isometries as a Lie subgroup. But usually this invariant metric has more symmetries than those given by the original action. Therefore the first question one may ask is when one can find a Riemannian metric so that the given action coincides with the action of the full group of isometries. This seems to be a difficult question to answer which depends very much on the orbit structure and the group itself. In this paper we give a sufficient condition that a subgroup action of a compact Lie group has an invariant metric which is not invariant under the full action of the group and figure out some aspects of the action and the orbit structure regarding the invariant Riemannian metric. In fact, according to our results, this is possible if there is a larger transformation group, containing the oringnal action and either having larger orbit somewhere or having exactly the same orbit structure but with an orbit on which a Riemannian metric is ivariant under the orginal action of the group and not under that of the larger one. Recently R. Saerens and W. Zame showed that every compact Lie group can be realized as the full group of isometries of Riemannian metric. [SZ] This answers a question closely related to ours but the situation turns out to be quite different in the two problems.

• 대한수학회보
• /
• 제53권4호
• /
• 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.

• 대한수학회논문집
• /
• 제35권2호
• /
• pp.613-623
• /
• 2020

The notion of quasi-Einstein metric in theoretical physics and in relation with string theory is equivalent to the notion of Ricci soliton in differential geometry. Quasi-Einstein metrics or Ricci solitons serve also as solution to Ricci flow equation, which is an evolution equation for Riemannian metrics on a Riemannian manifold. Quasi-Einstein metrics are subject of great interest in both mathematics and theoretical physics. In this paper the notion of Ricci 𝜌-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3-dimensional almost Kenmotsu Einstein manifold M is a 𝜌-soliton, then M is a Kenmotsu manifold of constant sectional curvature -1 and the 𝜌-soliton is expanding with λ = 2.