Affine spheres and convex \(\mathbb{R}\mathbb{P}^n\)-manifolds (Q2731067)
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scientific article; zbMATH DE number 1625515
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Affine spheres and convex \(\mathbb{R}\mathbb{P}^n\)-manifolds |
scientific article; zbMATH DE number 1625515 |
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28 October 2001
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projectively flat structures
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affine spheres
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Affine spheres and convex \(\mathbb{R}\mathbb{P}^n\)-manifolds (English)
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The author studies the differential geometry for manifolds with projectively flat connection and their realization in affine hypersurface theory. It is well known that, for dimension at least 3, such realizations give affine spheres, while the situation is more complicated in dimension 2. Here the author studies such structures on compact oriented surfaces of higher genus.NEWLINENEWLINENEWLINEReviewer's remark: There are local results for projectively flat surfaces in a recent thesis: \textit{Thomas Binder}, Two Codazzi problems for relative surfaces, Shaker Verlag Aachen (2002; Zbl 1015.53003).
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