Pseudosphere

In differential geometry, the term pseudo- sphere for different areas of use, which have a constant negative Gaußkrümmung:

• A hyperboloid,
• A Traktrikoid ( the surface of revolution of a tractrix ) or
• A theoretical surface of constant negative curvature.

Theoretical pseudosphere

In the abstract interpretation of a pseudo- sphere with radius R is a surface with constant Gaussian curvature ( precisely a complete, simply connected surface of curvature ), in analogy to a sphere with radius R, which is a surface with Gaussian curvature.

The term was coined in 1868 by Eugenio Beltrami introduced hyperbolic geometry in his work models.