Lines of curvature near umbilical points on surfaces immersed in \(\mathbb{R}^ 4\) (Q1894604)
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scientific article; zbMATH DE number 780911
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lines of curvature near umbilical points on surfaces immersed in \(\mathbb{R}^ 4\) |
scientific article; zbMATH DE number 780911 |
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Lines of curvature near umbilical points on surfaces immersed in \(\mathbb{R}^ 4\) (English)
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2 August 1995
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The authors study the principal configurations (the set formed by umbilical points and families of lines of maximal and minimal curvatures) of pairs consisting of an immersion of a compact orientable surface in a 4-space and a smooth unitary vector field normal to the immersed surface. They prove a genericity theorem for certain types of pairs which are defined by the Darboux conditions at umbilical points.
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structural stability
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principal configurations
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umbilical points
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