On the minimal area on membranes: Application of the theory of rectilinear congruence \(C\) (Q2771156)
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scientific article; zbMATH DE number 1705257
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the minimal area on membranes: Application of the theory of rectilinear congruence \(C\) |
scientific article; zbMATH DE number 1705257 |
Statements
13 June 2002
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rectilinear congruence
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minimal surfaces
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system of partial differential equations
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On the minimal area on membranes: Application of the theory of rectilinear congruence \(C\) (English)
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The authors study special categories of rectilinear congruences \(C\) whose focal surfaces are minimal. They derive a system of partial differential equations for four functions \(e,f,g\) and \(\rho\) determining the rectilinear congruence. This system consists of two equations which must be satisfied for \(e,f,g\) and \(\rho\) describing a rectilinear congruence and two other equations being the condition that the focal surfaces are minimal. In some special cases the authors solve this system of partial differential equations.
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