- In geometry, a
pseudosphere is a
surface with
constant negative Gaussian curvature. A
pseudosphere of
radius R is a
surface in R 3 {\displaystyle \mathbb...
- non-Euclidean
geometry by
modeling it on a
surface of
constant curvature, the
pseudosphere, and in the
interior of an n-dimensional unit sphere, the so-called Beltrami–Klein...
-
opposite each
other are
identified (considered to be the same). The
pseudosphere has the
appropriate curvature to
model hyperbolic geometry. The simplest...
- asymptote: the
pseudosphere.
Studied by
Eugenio Beltrami in 1868, as a
surface of
constant negative Gaussian curvature, the
pseudosphere is a
local model...
- that
lacks a
boundary with constant,
positive Gaussian curvature. The
pseudosphere is an
example of a
surface with
constant negative Gaussian curvature...
-
singular due to the
Hilbert embedding theorem. In the
simplest case, the
pseudosphere, also
known as the tractroid,
corresponds to a
static one-soliton, but...
-
surfaces of
class C2
immersed in R3, but
breaks down for C1-surfaces. The
pseudosphere has
constant negative Gaussian curvature except at its
boundary circle...
-
plane can be
placed onto a
pseudosphere and
maintain angles and
hyperbolic distances, as well as be bent
around the
pseudosphere and
still keep its properties...
-
examples of
generalized pseudospheres.
There is a
correspondence between embedded surfaces of
constant curvature -1,
known as
pseudospheres, and
solutions to...
-
surface with
constant negative curvature that can be
created by
twisting a
pseudosphere. It is
named after Ulisse Dini and
described by the
following parametric...
