A NOTE ON SURFACES IN THE NORMAL BUNDLE OF A CURVE

• 발행기관: 충청수학회
• 저자명: Doohann Lee HeungSu Yi
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 27, No. 2, 211~218쪽, 전체 8쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2014.05.30

영문 초록

In 3-dimensional Euclidean space, the geometric ¯g- ures of a regular curve are completely determined by the curvature function and the torsion function of the curve, and surfaces are the fundamental curved spaces for pioneering study in modern geom-etry as well as in classical di？？erential geometry. In this paper, we de¯ne parametrizations for surface by using parametric functions whose images are in the normal plane of each point on a given curve, and then obtain some results relating the Gaussian curva-ture of the surface with curvature and torsion of the given curve. In particular, we ¯nd some conditions for the surface to have either nonpositive Gaussian curvature or nonnegative Gaussian curvature.

목차

1. Introduction

2. Curvatures of surfaces in the normal bundle of a curve

3. Curvature of a surface de¯ned by a homogeneous normal sectional parametrization