JÁNOS PALLAGI , BENEDEK SCHULTZ , JENÖ SZIRMAI Equidistant Surfaces in H 2 × R Space

Visualization of Geodesic Curves , Spheres and Equidistant Surfaces in S 2 × R Space

The S2×R geometry is derived by direct product of the spherical plane S2 and the real line R. In [9] the third author has determined the geodesic curves, geodesic balls of S2×R space, computed their volume and defined the notion of the geodesic ball packing and its density. Moreover, he has developed a procedure to determine the density of the geodesic ball packing for generalized Coxeter space...

ÁNOS P ALLAGI , B ENEDEK S CHULTZ , J ENÖ S ZIRMAI On Regular Square Prism Tilings in S̃L 2 R Space On Regular Square Prism

The SL2R Lie-group consists of the real 2× 2 matrices ( d b c a ) with unit determinant ad − cb = 1. The S̃L2R geometry is the universal covering group of this group, and is a Lie-group itself. Because of the 3 independent coordinates, S̃L2R is a 3-dimensional manifold, with its usual neighbourhood topology. In order to model the above structure on the projective sphere PS3 and space P3 we introd...

The role of GABAergic mechanisms in the regulation of cochlear dopamine release

Hyperbolic surfaces of $L_1$-2-type

In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.

On the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space

The theory of the isoptic curves is widely studied in the Euclidean plane E2 (see [1] and [13] and the references given there). The analogous question was investigated by the authors in the hyperbolic H2 and elliptic E2 planes (see [3], [4]), but in the higher dimensional spaces there is no result according to this topic. In this paper we give a natural extension of the notion of the isoptic cu...