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| WEIERSTRASS REPRESENTATION FOR SURFACES WITH PRESCRIBED NORMAL GAUSS MAP AND GAUSS CURVATURE IN $H^{3}$ |
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Citation： |
SHI Shuguo.WEIERSTRASS REPRESENTATION FOR SURFACES WITH PRESCRIBED NORMAL GAUSS MAP AND GAUSS CURVATURE IN $H^{3}$[J].Chinese Annals of Mathematics B,2004,25(4):567~586 |
| Page view： 1295
Net amount： 903 |
Authors： |
SHI Shuguo; |
Foundation： |
Project supported by the 973 Project of the Ministry of Science and Technology of China and the
Science Foundation of the Ministry of Education of China. |
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| Abstract： |
The author obtains a Weierstrass representation for surfaces
with prescribed normal Gauss map and Gauss curvature in
$H^{3}$. A differential equation about the hyperbolic
Gauss map is also obtained, which characterizes the relation among the
hyperbolic Gauss map, the normal Gauss map and Gauss curvature.
The author discusses the harmonicity of the
normal Gauss map and the hyperbolic Gauss map
from surface with constant Gauss curvature in $H^{3}$ to
$S^{2}$ with certain altered conformal metric. Finally, the
author considers the surface whose normal Gauss map is conformal and
derives a completely nonlinear differential equation of
second order which graph must satisfy. |
Keywords： |
Hyperbolic space, Hyperbolic Gauss map, Normal Gauss map, Weierstrass
representation, Harmonic map |
Classification： |
53C42, 53A10 |
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