Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations
arXiv:1105.3642 · doi:10.2478/S11533-012-0044-4
Abstract
On any space-like W-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 W-surfaces in Minkowski space. We apply this theory to linear fractional space-like W-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 W-surfaces.
16 pages; 5 references added. arXiv admin note: substantial text overlap with arXiv:1105.3652