Cayley surfaces in affine differential geometry (Q1825441)
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scientific article; zbMATH DE number 4120918
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cayley surfaces in affine differential geometry |
scientific article; zbMATH DE number 4120918 |
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Cayley surfaces in affine differential geometry (English)
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1989
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A Cayley surface in affine space \({\mathbb{R}}^ 3\) is, by definition, the graph of a cubic polynomial, say, \(z=xy-y^ 3/3\quad or\quad z=xy-x^ 3/3.\) The purpose of the present paper is to characterize a Cayley surface as a nondegenerate surface in \({\mathbb{R}}^ 3\) whose cubic form in nonzero and parallel relative to the induced connection of the surface.
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Cayley surface
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cubic polynomial
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cubic form
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induced connection
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