What Is the Gauss Embedding Theorem Mentioned in the Video Talk?

[The Tortoise-Man]

Does anybody know to which "Gauss embedding theorem" the speaker in this video talk at minute 14 (point 5. in the displayed notes) is refering too? Sounds to be a standard result in differential geometry, but after detailed googling I found nothing to which the speaker may refering too in the linked video. Any ideas?

 

[Hill]

Any ideas?

Nash embedding theorems?