Characterizations Of Spherical Curves With Structure Function

The theory of spherical geometry plays a special role in the study of geometry. Based on the fundamental theorem of the space curves, except for the position, curves are only determined by their natural equation. In addition to curvature and torsion, a variable called structure function is determined in this thesis to characterize curves, which is similar to the nature equation.In the second chapter, the concepts, the main theorems and corollaries of the vector function and the basic theory of curves are introduced. The third chapter is the main chapter. In this chapter, by introducing the structure functions ?(s), ?(s) and g(s), the curvature ?(s) and torsion ?(s) of spherical curves are discussed, and it is obtained that the spherical curvature A(s) with the spherical frame is geodesic curvature ?q; by the nature of the special curves in differential geometry, a solution of nonlinear differential equation is gained, which iswhere c, and c2 are arbitrary constants, and c12+c22=1. At last, by discussing the properties of special spherical curves, such as the spherical spiral, some special conclusions are obtained.