TITLE: Can a hyperbolic surface be isometrically embedded into $\mathbb R^4$?
QUESTION [6 upvotes]: Can a complete hyperbolic surface be isometrically embedded into flat $\mathbb R^4$?

REPLY [6 votes]: It is known that the hyperbolic plane can be isometrically immersed in $E^5$ (and isometrically embedded in $E^6$). Existence of an isometric immersion into $E^4$ is an open problem. Thus, the answer to your question is "unknown".