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

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Ganchev G., Mihova V.

Open Mathematics

2013

tom 11

nr 1

133-148

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.

Ograniczanie wyników

1 Open Mathematics

1 Ganchev G.

1 Mihova V.

1 2013

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