# An explicit (maybe algebraic) isometric embedding of the double torus with constant curvature K = -1

The following question is related to this previous question, Canonical immersion of the double torus:

Is there any known explicit (maybe algebraic) isometric embedding of a genus 2 surface endowed with a metric of constant curvature K = -1 into a Hilbert space of finite dimension?

• Isometric embedding into where? – Deane Yang Jul 30 at 23:23
• Into a Hilbert space of finite dimension. – Mauro Patrão Jul 31 at 2:27
• Or, to be more concrete, into $\mathbb{R}^n$ for some $n > 0$? – Deane Yang Jul 31 at 2:51
• Into an R^n with a fixed inner product. – Mauro Patrão Jul 31 at 19:12
• I’m pretty sure none is known, and it’s an open question whether any such “explicit” embedding or evening just immersion exists. – Deane Yang Jul 31 at 22:11