Wikipedia:Reference desk/Archives/Mathematics/2018 February 1

= February 1 =

embedding of different geometries
S² can obviously be embedded in E³ or H³.

E² can be embedded in H³ (Horosphere).

A piece of H² can be embedded in E³ (Pseudosphere).

Can a piece of E² be embedded in S³? —Tamfang (talk) 11:33, 1 February 2018 (UTC)


 * See, which implies that a square flat torus (of two dimensions) embeds (smoothly) in S$3$. Since a piece of E$2$ embeds in the flat torus, the answer to your question would be "yes".  If one permits non-smooth embeddings, even more becomes possible.  —Quondum 02:43, 2 February 2018 (UTC)


 * [slap forehead] —Tamfang (talk) 00:08, 3 February 2018 (UTC)