Pseudosphere
In differential geometry , the term pseudosphere is used for various surfaces that have a constant negative Gaussian curvature :
- a hyperboloid ,
- a tractricoid (the rotating surface of a tractrix ) or
- a theoretical surface of constant negative curvature.
Theoretical pseudosphere
In the abstract interpretation, a pseudosphere with radius is a surface with constant Gaussian curvature (precisely a complete , simply connected surface of this curvature), in analogy to a sphere with radius , which is a surface with Gaussian curvature .
The term was introduced in 1868 by Eugenio Beltrami in his work Models of Hyperbolic Geometry .
Web links
- Eric W. Weisstein : Pseudosphere . In: MathWorld (English).