On any space-like Weingarten surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for space-like Weingarten surfaces in Minkowski space. We apply this theory to linear fractional space-like Weingarten surfaces and obtain the natural non-linear partial differential equations describing them. We obtain a characterization of space-like surfaces, whose curvatures satisfy a linear relation, by means of their natural partial differential equations. We obtain the ten natural PDE’s describing all linear fractional space-like Weingarten surfaces.
@article{bwmeta1.element.doi-10_2478_s11533-012-0044-4,
author = {Georgi Ganchev and Vesselka Mihova},
title = {Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {133-148},
zbl = {1273.53014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0044-4}
}
Georgi Ganchev; Vesselka Mihova. Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations. Open Mathematics, Tome 11 (2013) pp. 133-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0044-4/
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