A sufficient condition for Teichmüller spaces to have smallest possible inner radii.
Nakanishi, Toshihiro, Velling, John A. (1993)
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Nakanishi, Toshihiro, Velling, John A. (1993)
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We consider surfaces in hyperbolic 3-space and their duals. We study flat dual surfaces in hyperbolic 3-space by using extended Legendrian dualities between pseudo-hyperspheres in Lorentz-Minkowski 4-space. We define the flatness of a surface in hyperbolic 3-space by the degeneracy of its dual, which is similar to the case of the Gauss map of a surface in Euclidean 3-space. Such surfaces are a kind of ruled surfaces. Moreover, we investigate the singularities of these surfaces and the...
Wilczyński, Władysław, Rzepecka, Genowefa (2015-11-26T16:01:41Z)
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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...