Bir eğri üzerindeki umbilik nokta çiftleri

This work consists of six chapters: The first chapter is the introduction section. In the second chapter; some basic definitions and theorem have been introduced. In the third chapter; an extensive analysis of the surfaces have been made and the existence of umbilical points on the surfaces are analysed. In the fourth chapter; the surface made of the curves which are built up with umbilical points is defined, basic forms of the surface are found, Gauss and mean curves were given, and principle curvature lines are displayed. Also, the tub surfaces were described and The tub surfaces with Darboux Frame were analysed. The fifth chapter is the original part of the thesis, in which center curve of tube surfaces given with Darboux frame are chosen as a special curve which is built up with umbilical points, and according to those data, Gauss and mean curves are calculated and it is analysed if the surface is Weingarten. In the last chapter; the results were given.