- as a
sphere of
imaginary radius,
embedded in a
Minkowski space. A
pseudospherical surface is a
generalization of the pseudosphere. A
surface which is...
-
minimal surfaces,
ruled surfaces, non-orientable surfaces, quadrics,
pseudospherical surfaces,
algebraic surfaces, and
other types of surfaces. Catalan's...
- of
pseudospherical surfaces introduced by L.
Bianchi and A.V. Bäcklund in the 1880s. This is a
geometrical construction of a new
pseudospherical surface...
- This
breather pseudospherical surface corresponds to a
solution of a non-linear wave-equation....
-
constant Gaussian curvature K = −1, also
called pseudospherical surfaces.
Consider an
arbitrary pseudospherical surface.
Across every point on the surface...
- a
saddle point.
Hyperbolic plane geometry is also the
geometry of
pseudospherical surfaces,
surfaces with a
constant negative Gaussian curvature. Saddle...
-
Following is a list of some
mathematically well-defined shapes.
Cubic plane curve Quartic plane curve Fractal Conic sections Unit
circle Unit hyperbola...
- a
surface has a
constant negative Gaussian curvature, then it is a
pseudospherical surface and the
geometry of the
surface is
hyperbolic geometry. The...
- of
constant curvatures,
Sophus Lie (1879)
found a way to
derive new
pseudospherical surfaces from a
known one. Such
surfaces satisfy the Sine-Gordon equation:...
- Her dissertation, A
Brief Account of the
Historical Development of
Pseudospherical Surfaces from 1827 to 1887,
concerned the
history of non-Euclidean...
