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Results tagged with embeddings
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user 1345
8
votes
Transitive embedding of the projective plane $\Bbb R P^2$ into the $4$-sphere
One might be able to construct similar smaller dimensional embeddings using fibrations $S^1\to \mathbb{RP}^{2n+1}\to \mathbb{CP}^n$ and $\mathbb{RP}^3\to \mathbb{RP}^{4n+3}\to \mathbb{HP}^n$, but I haven't … checked if they give smaller embeddings with isometric actions. …
- 68.9k
8
votes
Can a knotted sphere isometrically embed into $\mathbb R^3$?
A spun knot will give a 2-sphere embedded in $\mathbb{R}^4$ whose intrinsic metric embeds into $\mathbb{R}^3$ isometrically as a surface of revolution.
Take a tangle $T$ in $\mathbb{R}^3_+$ with two e …
- 68.9k
4
votes
Under what conditions can an orientable Riemannian 3-manifold be defined implicitly?
This is too long for a comment.
If you want $0$ to be a regular value of $f$, then this should be possible iff there is a smooth isometric embedding to $R^n$ with trivial normal bundle (for any dimens …
- 68.9k