On the Differential Geometry of Surfaces in R3
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, som...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2002
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| Online Access: | http://ndltd.ncl.edu.tw/handle/40186506021521819164 |
| Summary: | 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.
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