Darboux curves on surfaces I (Q520623)
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scientific article; zbMATH DE number 6701581
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Darboux curves on surfaces I |
scientific article; zbMATH DE number 6701581 |
Statements
Darboux curves on surfaces I (English)
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5 April 2017
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In this paper a class of curves on a surface is investigated. These curves are characterized by the property that their osculating spheres are tangent to the surface. Such curves are referred to as `Darboux curves'. In this paper Darboux curves are characterized under the Lorentz group. This way, such curves can even be described as geodesics in a 3-dimensional sub-variety of some quadric. This thorough investigation of such curves is based on the space of oriented spheres which can be viewed as a hyperquadric of the 5-dimensional Lorentz space.
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Darboux curve
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canal surface
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conformal geometry
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space of spheres
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Lorentz group
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