Minimal submanifolds geometry

This master thesis consists of five chapters. In the first chapter, we survey historical development of the subject and give an outline for the context of this thesis. In the second chapter, some basic concepts are given about topology and manifolds. In the third chapter, methods for finding the first variation form are presented. In the fourth chapter, that constitutes the main part of the thesis, characterizations are obtained if the space form is Euclidean and sphere in the minimal submanifolds. In addition, this section presents a minimal surface example of the Helicoid and Catenoid surfaces of three dimensional Euclidean space. Finally, in the fifth chapter, some sections on Rigidity theorem are presented, and then methods for Rigidity theorem calculations are presented.