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

• Autorzy: Georgi Ganchev , Vesselka Mihova
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Space-like W-surfaces in Minkowski space; Natural parameters on space-like W-surfaces in Minkowski space; Natural PDE’s of space-like W-surfaces in Minkowski space

Kategorie tematyczne

• 53A05: Surfaces in Euclidean space
• 53A10: Minimal surfaces, surfaces with prescribed mean curvature

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 1
• Strony: 133-148

Daty

wydano

2013-01-01

online

2012-10-24

Twórcy

autor

Georgi Ganchev

• Acad. G. Bonchev

autor

Vesselka Mihova

• University of Sofia

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0044-4