Geometry and singularities of spatial and spherical curves

Abstract

In the first part of this dissertation the spherical evolute, the spherical involute, the spherical orthotomic and the spherical antiorthotomic are investigated and their local diffeomorphic types are determined. The concept of the spherical conic is introduced. It is proven that the incident angle and reflection angle are equal for the spherical conic. The necessary and sufficient conditions for the spherical conic to be a circle are given. In the second part of this dissertation the ruled surfaces of normals and binormals of a regular space curve are locally classified under the left-right action according to the types of the curve. For this purpose some results are obtained on the relationship of the powers of terms in the Taylor series of an invertible function and its inverse.