Pseudosphere

Definitions

  • Webster's Revised Unabridged Dictionary
    • n Pseudosphere (Geom) The surface of constant negative curvature generated by the revolution of a tractrix. This surface corresponds in non-Euclidian space to the sphere in ordinary space. An important property of the surface is that any figure drawn upon it can be displaced in any way without tearing it or altering in size any of its elements.
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Century Dictionary and Cyclopedia
    • n pseudosphere A surface of constant negative curvature.
    • n pseudosphere A sphere in non-Euclidean geometry.
    • n pseudosphere The surface generated by the revolution of the tractrix about its asymptote.
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Etymology

Webster's Revised Unabridged Dictionary
Pseudo-, + sphere,

Usage


In science:

With our choice the leaves S are foliated by pseudospheres, i.e space-like orbits of SO(2, 1) which are non-compact and of constant negative curvature.
On the SO(2,1) symmetry in General Relativity
We note in particular that the univariate and bivariate normal distributions have constant negative scalar curvature, so geometrically they constitute parts of pseudospheres.
Information geometric neighbourhoods of randomness and geometry of the McKay bivariate gamma 3-manifold
We define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales.
Pseudospherical surfaces on time scales
Two special cases, namely dicrete pseudospherical surfaces and smooth pseudosperical surfaces are consistent with this description.
Pseudospherical surfaces on time scales
In this paper we propose such formulation for pseudospherical immersions (surfaces of constant negative Gaussian curvature).
Pseudospherical surfaces on time scales
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