| Numéro |
J. Phys. Colloques
Volume 51, Numéro C7, Décembre 1990
International Workshop on Geometry and Interfaces
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|
|---|---|---|
| Page(s) | C7-163 - C7-168 | |
| DOI | https://doi.org/10.1051/jphyscol:1990716 | |
International Workshop on Geometry and Interfaces
J. Phys. Colloques 51 (1990) C7-163-C7-168
DOI: 10.1051/jphyscol:1990716
I. Mathematisches Institut der Freien Universität Berlin, Arnimallee 3, D-1000 Berlin 33, F.R.G.
© EDP Sciences 1990
J. Phys. Colloques 51 (1990) C7-163-C7-168
DOI: 10.1051/jphyscol:1990716
H. HOPF'S QUADRATIC DIFFERENTIAL AND A WEIERSTRASS FORMULA FOR GENERAL SURFACES AND SURFACES OF CONSTANT MEAN CURVATURE
F. GACKSTATTERI. Mathematisches Institut der Freien Universität Berlin, Arnimallee 3, D-1000 Berlin 33, F.R.G.
Abstract
Using H. Hopf's quadratic differential Φ dw2 we find a representation formula for general surfaces in ℝ3 similar to the classical Weierstrass formula for minimal surfaces. For surfaces of constant mean curvature with prescribed Φ dw2 an integrability condition with the properties of a conservation equation is derived. We continue the work of K. Kenmotsu on surfaces of prescribed mean curvature.
© EDP Sciences 1990