A surface of constant negative curvature formed by rotating a tractrix (, ) around its asymptote (; see Fig.).
The line element in semi-geodesic coordinates has the form:
(the line is a geodesic); while in isothermal coordinates it has the form:
Every surface of constant negative curvature can be locally imbedded in the pseudo-sphere. The intrinsic geometry of a pseudo-sphere coincides locally with hyperbolic geometry (see Beltrami interpretation).
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Pseudo-sphere. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Pseudo-sphere&oldid=16805