# dg.differential geometry – Immersion of a part of the hyperbolic plane in \$mathbb{R}^3\$

I know that the pseudosphere is a regular surface with Gaussian curvature $$-1$$ that is not complete, also this surface is not complete. Hilbert’s theorem ensures that there is no isometric immersion of the hyperbolic plane $$mathbb{H}^2$$ in $$mathbb{R}^3$$, but if we remove a point from the hyperbolic plane, can it be immersed isometrically in $$mathbb{R}^3$$? Who could it be?