A Survey on a Classical Result in the Studies of Minimal Submanifolds
碩士 === 國立交通大學 === 應用數學系所 === 107 === The famous result on minimal submanifolds in a unit sphere of higher dimension due to S.S. Chern, M. Do Carmo, and S. Kobayashi has two assertions. One assertion is about the length of the second fundamental form which is a constant under some restrictions, and t...
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| Format: | Others |
| Language: | en_US |
| Published: |
2019
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| Online Access: | http://ndltd.ncl.edu.tw/handle/3vg3nx |
| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 107 === The famous result on minimal submanifolds in a unit sphere of higher dimension due to S.S. Chern, M. Do Carmo, and S. Kobayashi has two assertions. One assertion is about the length of the second fundamental form which is a constant under some restrictions, and the other assertion is about there exist two types of minimal submanifolds satisfying the constant which is mentioned on the former assertion.
In this thesis, we try our best to understand the assertions which are the main mathematical result due to the above mentioned mathematicians and to present all minute details in the mathematical arguments, so that our thesis could serve as a guideline (or a steppingstone) for any potential beginning reader who is interested in taking a first look at such a classical result in the area of minimal submanifold.
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