The characterizations of canal surfaces

This thesis consists of four chapters. The first chapter is devoted to the introduction. In the second chapter, some basic definitions and concepts about curves and surfaces in Euclidean space are given. In the third chapter, firstly some basic concepts and definitions about canal surfaces are given. And then some calculations about the coefficients of the first, second and third fundamental forms, the mean curvature, Gaussian curvature, the second Gaussian curvature, the principal curvatures and the relationships about these curvature functions are given. Also some characterizations for flat canal surface, minimal canal surface and canal surface whose the second Gaussian curvature vanishes are obtained. Finally some characterizations about (K, H), (K, KII ) and (H, KII ) Weingarten canal surfaces are given In the last chapter, discussion and results are given.