Spherical Curves And Representation In Euclidean 3-space

Spherical curve plays an important role in differential geometry and industrial application.Special curve is a hot topic in the study of modern differential geometry.So it is worth for us to research it.There are four chapters in this thesis.Chapter one is an introduction part.We introduce the development of geometry,the main research content of modern differential geometry and the research significance of this article simply.In the second chapter,introducing the basic knowledge which is going to be used,such as Euclid inner product,basic theory of space curves and the definition and quality of some special curves.Chapter three is the main chapter.By introducing the structure functions f(s),?(s)and g(s),the spherical curvature is researched.Using the spherical Frenet frame and spherical curvature,we research the characterization of some spherical curves in Euclidean 3-space,rectifying curve,Bertrand curve,Mannheim curve,center trace of osculating sphere on spherical surfaces.Chapter four is the summary of this paper.