On the curvature lines of surfaces in a Euclidean space \(E^4\) (Q2705018)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the curvature lines of surfaces in a Euclidean space \(E^4\) |
scientific article |
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20 March 2001
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lines of curvature
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minimal surfaces
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Chen-surfaces
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On the curvature lines of surfaces in a Euclidean space \(E^4\) (English)
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In this work the lines of curvature of a surface in the Euclidean 4-space \(E^4\) are considered. The author uses the method of the moving frame. After obtaining the corresponding differential equation in a new form he studies various properties of the lines of curvature of special classes of surfaces, among them the surfaces of Chen (i.e. surfaces for which the vector of the mean curvature vanishes), the minimal surfaces and the surfaces whose lines of curvature form an harmonic quadruple of curves. The work is nice and well organized.
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