An introduction to integrable difference and differential geometries: Affine spheres, their natural generalization and discretization (Q2781674)
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scientific article; zbMATH DE number 1721617
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An introduction to integrable difference and differential geometries: Affine spheres, their natural generalization and discretization |
scientific article; zbMATH DE number 1721617 |
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20 January 2003
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affine sphere
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Tzitzeica transformation
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Bäcklund transformation
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An introduction to integrable difference and differential geometries: Affine spheres, their natural generalization and discretization (English)
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The main goal of the paper is discretization of affine geometries. In 1907 Tzitzeica introduced the classical (proper) affine spheres. It is shown how these surfaces may be discretized in a natural geometric manner. The construction results in an integrable discrete version of the Tzitzeica-equation related to affine spheres. It is demonstrated how discrete surfaces may be generated by application of the Tzitzeica transformation to affine spheres. These discrete surfaces contain the class of discrete affine spheres constructed in the above mentioned geometric manner. As a by-product, a discrete version of the Tzitzeica transformation is obtained.NEWLINENEWLINEFor the entire collection see [Zbl 0974.00040].
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