Timeline for What is a specific example of a Calabi-Yau manifold? are there simple ones like a 6-torus, $T^6=(S^1)^6$ or $S^3\times T^3$

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May 25, 2022 at 11:39	comment	added	Michael Seifert		@EdenZane: a torus does have to have extrinsic curvature if it's embedded in a higher-dimensional Euclidean space. But it is possible to mathematically define a torus via these sorts of identifications without reference to a higher-dimension space in which it's embedded, and in this case it has no intrinsic curvature (and it's meaningless to talk about extrinsic curvature). If you want more details on this, I would encourage you to ask it separately (probably over at Mathematics rather than here.)
May 25, 2022 at 4:39	comment	added	Eden Zane		what I believe is that a torus is never flat - please correct me if I am wrong.
May 25, 2022 at 4:38	comment	added	Eden Zane		I am skeptical on whether we can have any physical mapping like "identifying" opposite edges of a parallelopiped, in reality people talk about circles when they are asked how can they identify two opposite edges of a square, but then you can never talk about the space being flat i guess. When you realize the "identification of opposite edges" as a circle, it is introducing some curvature.
May 24, 2022 at 16:51	vote	accept	Eden Zane
May 24, 2022 at 15:14	history	edited	Michael Seifert	CC BY-SA 4.0	added 348 characters in body
May 24, 2022 at 14:25	history	answered	Michael Seifert	CC BY-SA 4.0