made a study of honeycombs whose cells are equal regular polytopes in spaces of positive, zero, and negative curvature. The spherical and Euclidean honeycombs had already been described by Schlaf li (1855), but the only earlier mention of the hyperbolic honeycombs was when Stringham (1880, pp. 7, 12, and errata) discarded them as "imaginary figures", or, for the two-dimensional case, when Klein...

This study presents a new approach for physical and material modeling of space frame-raft-soil system. The physical modeling consists of a modified Thimoshenko beam bending element with six degrees of freedom per node to model the beams and columns of the superstructure, a modified Mindlin's plate bending element with five degrees of freedom per node to represent the structural slabs and raft, ...

The longitudinal Doppler shift is a measure of hyperbolic distance. Transformations of uniform motion are determined by the Doppler shift, while its square root transforms to a uniformly accelerated frame. A time-velocity space metric is derived, by magnifying the Beltrami coordinates with the geometric time, which is similar to the one obtained by Friedmann using Einstein’s equations in which ...

The space of broken hyperbolic structures generalizes the usual Teichmüller space of a punctured surface, and the space of projectivized broken measured foliations–or equivalently, the space of projectivized affine foliations of a punctured surface–likewise admits a generalization to projectivized broken measured foliations. Just as projectivized measured foliations provide Thurston's boundary ...

we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...

Let (Xi, di), i = 1, 2, be proper geodesic hyperbolic metric spaces. We give a general construction for a " hyperbolic product " X1× h X2 which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity.

the present paper studies the possibility of propagation of torsional surface waves in an inhomogeneous anisotropic layer lying between two heterogeneous half-spaces (upper and lower half-space). both the half-spaces are assumed to be under compressive initial stress. the study reveals that under the assumed conditions, a torsional surface wave propagates in the medium. the dispersion relation ...

We introduce the (2+1)-spacetimes with compact space of genus g ≥ 0 and r gravitating particles which arise by Minkowskian suspensions of flat or hyperbolic cone surfaces, by distinguished deformations of hyperbolic suspensions and by patchworking of suspensions. Similarly to the matter-free case, these spacetimes have nice properties with respect to the canonical Cosmological Time Function. Wh...

Which slopes can or cannot appear as Seifert fibered slopes for hyperbolic knots in the 3-sphere S? It is conjectured that if r -surgery on a hyperbolic knot in S yields a Seifert fiber space, then r is an integer. We show that for each integer n ∈ Z, there exists a tunnel number one, hyperbolic knot Kn in S 3 such that n-surgery on Kn produces a small Seifert fiber space. AMS Classification 57...

We describe a new proof of the complete integrability of the two related dynamical systems: the billiard inside the ellipsoid and the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose nonparameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperb...