On the centroaffine family of relative normals and their minimal surfaces (Q2781775)
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scientific article; zbMATH DE number 1726603
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the centroaffine family of relative normals and their minimal surfaces |
scientific article; zbMATH DE number 1726603 |
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29 April 2002
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relative geometry
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affine differential geometry
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affine extremal surfaces
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0.8949075
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0.8850412
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0.8772381
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0.8763468
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0.8762123
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On the centroaffine family of relative normals and their minimal surfaces (English)
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The paper gives an overview of several special classes of relative normals and discusses the notion of minimality in each of the cases. In particular it is recalled that the classical Blaschke normal and the Euclidean normal can be seen as belonging to a 1-parameter family of relative normals. For each member of this family, the first variation formulas for the 2 possible volume forms (which coincide for the Blaschke normal) are given. NEWLINENEWLINENEWLINEIt is also shown that there exists a similar 1-parameter family of relative normals relating the centroaffine and the Blaschke normalisations. In this case also the first variations of both possible volume forms are computed.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00037].
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