A topological proof of the Arnold four cusps theorem (Q2903267)
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scientific article; zbMATH DE number 6064188
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A topological proof of the Arnold four cusps theorem |
scientific article; zbMATH DE number 6064188 |
Statements
A topological proof of the Arnold four cusps theorem (English)
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8 August 2012
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generic surface
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Whitney cusp
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elliptic metric
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bending angle
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caustic
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semi-cubical vertice
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0.85751253
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0.85674894
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0.85451853
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0.8544356
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0.85385275
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0.8532699
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0.84940445
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\textit{V. I. Arnold} in [Rev. Mat. Univ. Complutense Madr. 8, No. 1, 109--119 (1995; Zbl 0973.53501)] proved a theorem stating that on a generic Riemannian surface which is sufficiently close to a sphere has at least four semi-cubical vertices. The author proves the same fact using the Morse theory and replacing the condition of closeness to the sphere by some less restrictive geometric hypothesis.
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