# which surfaces have (for a large area) a constant negative curvature?

There is no surface in $R^3$ that can represent the complete hyperbolic plane (Hilberts theorem) so we always have to do with a surface that is not completely equivalent, has a cusp somewhere, but in most publications on hyperbolic geometry, it is almost given that the tracioid (tractrix rotated about its asymptope) is a surface that has a constant negative curvature, and in many publications "tracioid" and "pseudosphere" are used interchangable.

But I am wondering are there other surfaces that have a constant negative curvature?

I did some searching and did find: