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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#Tractricoid).

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

See Torus § Flat torus, which implies that a square flat torus (of two dimensions) embeds (smoothly) in S³. Since a piece of E² 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)[reply]

[slap forehead]

Resolved

—Tamfang (talk) 00:08, 3 February 2018 (UTC)[reply]