On the Differential Geometry of Surfaces in R3

• Main Author: 余珮甄
• Other Authors: 蔡東河
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/40186506021521819164

碩士 === 國立中正大學 === 數學研究所 === 90 === Abstract The main contents of this thesis is about surface in R3. We introduce the first and second fundamental forms of a given surface S of R3 and use them to define the various curvature of S. For various surface curvature, some are intrinsic and some are extrinsic. We shall see that the Gauss curvature is intrinsic, which is one of the most important theorem in surface theorem. On the other hand, the mean curvature is extrinsic. We introduce the Riemannian curvature tensor, and derive the fundamental equations of Gauss and Codazzi-Mainardi. We use them to prove that the Gauss curvature is intrinsic Finally we discuss straight lines in surface called geodesics and study the isometry theorem.