Displaying similar documents to “Curves and surfaces in hyperbolic space”

Boundaries of right-angled hyperbolic buildings

Jan Dymara, Damian Osajda (2007)

Fundamenta Mathematicae

Similarity:

We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.

Legendrian dual surfaces in hyperbolic 3-space

Kentaro Saji, Handan Yıldırım (2015)

Annales Polonici Mathematici

Similarity:

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...

On continuous solutions to linear hyperbolic systems

Małgorzata Zdanowicz, Zbigniew Peradzyński (2005)

Annales Polonici Mathematici

Similarity:

We study the conditions under which the Cauchy problem for a linear hyperbolic system of partial differential equations of the first order in two independent variables has a unique continuous solution (not necessarily Lipschitz continuous). In addition to obvious continuity assumptions on coefficients and initial data, the sufficient conditions are the bounded variation of the left eigenvectors along the characteristic curves.