Algebraic Hypersurfaces of Degree Three in the Unit Sphere
碩士 === 國立交通大學 === 應用數學系所 === 103 === In this thesis, we want to construct a certain class of algebraic minimal hypersurface M^{n} of degree three in the unit sphere S^{n+1}. The idea is to find a class of special solutions to the equation Σϕiϕijϕj-|∇ϕj|^{2}Δϕ = 0 mod ϕ, where ϕ:R^{n+2}→R is a homoge...
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| Format: | Others |
| Language: | en_US |
| Published: |
2015
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| Online Access: | http://ndltd.ncl.edu.tw/handle/77897587646660763035 |
| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 103 === In this thesis, we want to construct a certain class of algebraic minimal hypersurface M^{n} of degree three in the unit sphere S^{n+1}. The idea is to find a class of
special solutions to the equation Σϕiϕijϕj-|∇ϕj|^{2}Δϕ = 0 mod ϕ, where ϕ:R^{n+2}→R is a homogeneous irreducible polynomial of degree three. Using these special solutions, we find certain minimal hypersurfaces in explicit form with various dimensions.
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