pseudosphere
Sign in to saveIn geometry, a pseudosphere is a surface in \mathbb{R}^3. It is the most famous example of a pseudospherical surface. A pseudospherical surface is a surface piecewise smoothly immersed in \mathbb{R}^3 with constant negative Gaussian curvature. A "pseudospherical surface of radius " is a surface in \mathbb{R}^3 having curvature −1/R2 at each point. Its name comes from the analogy with the sphere of radius , which is a surface of curvature 1/R2. Examples include the tractroid, Dini's surfaces, breather surfaces, and the Kuen surface.
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Encyclopedic overview
9 sectionsContents
- Tractroid
- Line congruence
- Universal covering space
- Hyperboloid
- Relation to solutions to the sine-Gordon equation
- See also
- References
- Further reading
- External links
In geometry, a pseudosphere is a surface in \mathbb{R}^3. It is the most famous example of a pseudospherical surface. A pseudospherical surface is a surface piecewise smoothly immersed in \mathbb{R}^3 with constant negative Gaussian curvature. A "pseudospherical surface of radius " is a surface in \mathbb{R}^3 having curvature −1/R2 at each point. Its name comes from the analogy with the sphere of radius , which is a surface of curvature 1/R2. Examples include the tractroid, Dini's surfaces, breather surfaces, and the Kuen surface.
The term "pseudosphere" was introduced by Eugenio Beltrami in his 1868 paper on models of hyperbolic geometry.
Excerpted from Wikipedia’s “pseudosphere” article, available under the CC BY-SA 4.0 licence.