Earticle

본 연구는 미국의 윌리엄 포사이드의 작품 ｢Synchronous Objects for One Flat Thing, Reproduced｣를 기하학적 시각으로 분석하는 것을 목적으로 한다. 이 작품은 온라인 플랫폼에 기반 한 디지털 작품으로서, 다양한 분야를 융합해 20가지 오브제를 제작했으 며 기하학적 형태를 활용하여 무용수들의 움직임과 공간적 상호작용을 다양하게 표현한 다. 본 연구에서는 기하학적 형태인 점, 선, 면을 기반으로 무용수들의 움직임을 분석함으 로써 예술과 기하학의 상호작용과 융합을 탐구한다. 무용수들이 서로 교차하는 부분이나 동기화된 움직임 등을 통해 공간상에서 다양한 패턴과 구조가 형성되는 것을 밝힌다. 따라서, 본 연구는 무용과 기하학의 결합을 분석함으로써 무용수들의 움직임과 무대 공간을 기하학적으로 분석하고 이해하는데 기여한다.

This study analyzes William Forside’s Synchronous Objects for One Flat Thing, Reproduced from a geometric perspective. This dance is a digital work presented through an online platform, which combines various fields to produce 20 objects. The work uses geometric forms to express dancers’ movements and spatial interactions in various ways. In our study, the interaction and fusion of art and geometry are explored by analyzing the dancers’ movements by means of geometric shapes such as points, lines, and planes. It analyzes how various patterns and structures are formed in space when dancers pass each other or make synchronized movements. Therefore, this study contributes to geometrically analyzing and understanding the dancers’ movements and their uses of stage space by combining dance and geometry.

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.

In this article, we derived Chen's inequality for warped product bi-slant submanifolds in generalized complex space forms using semisymmetric metric connections and discuss the equality case of the inequality. Further, we discuss non-existence of such minimal immersion. We also provide various applications of the obtained inequalities.

In early design stages structural form finding is of importance. Theses days the structural forms are forced to satisfy not only engineering criteria but also aesthetic concerns including symbolism. Geometric approach seems to provide many possibilities in generating creative forms as design alternatives for bridge structures. However, the increase in possibilities of geometric application didn't gather much attention from bridge designers who are focusing mainly on structural aspects. Prior to adopting the geometric approach, it is needed to review bridge structures in terms of geometric vocabulary. This study has proposed how to generate geometric forms of bridge structures in terms of geometric computing concepts.