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

Georgi Ganchev; Vesselka Mihova

Open Mathematics (2013)

  • Volume: 11, Issue: 1, page 133-148
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Georgi Ganchev, and Vesselka Mihova. "Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations." Open Mathematics 11.1 (2013): 133-148. <http://eudml.org/doc/269698>.

@article{GeorgiGanchev2013,
abstract = {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.},
author = {Georgi Ganchev, Vesselka Mihova},
journal = {Open Mathematics},
keywords = {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; space-like W-surfaces; Minkowski space; natural parameters on space-like W-surfaces; natural PDE's of space-like W-surfaces},
language = {eng},
number = {1},
pages = {133-148},
title = {Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations},
url = {http://eudml.org/doc/269698},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Georgi Ganchev
AU - Vesselka Mihova
TI - Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations
JO - Open Mathematics
PY - 2013
VL - 11
IS - 1
SP - 133
EP - 148
AB - 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.
LA - eng
KW - 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; space-like W-surfaces; Minkowski space; natural parameters on space-like W-surfaces; natural PDE's of space-like W-surfaces
UR - http://eudml.org/doc/269698
ER -

References

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