Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations

作者：Ganchev Georgi^*; Mihova Vesselka

来源：Central European Journal of Mathematics, 2013, 11(1): 133-148.

DOI：10.2478/s11533-012-0044-4

• Space-like W-surfaces in Minkowski space
• Natural parameters on space-like W-surfaces in Minkowski space
• Natural PDE%26apos
• s of space-like W-surfaces in Minkowski space

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%26apos;s describing all linear fractional space-like Weingarten surfaces.

• 出版日期2013-1