Timeline for When is a Riemannian manifold an open subset of a complete one?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2009 at 0:06 | comment | added | some guy on the street | @Mariano, yes, the half-cone is a classic of an orbifold; the nonsingular part is also an affine manifold. That is, you can build it out of paper. | |
| Dec 13, 2009 at 0:05 | history | edited | some guy on the street | CC BY-SA 2.5 |
adjusting to an edited question; Post Made Community Wiki
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| Dec 12, 2009 at 0:57 | comment | added | Jonas Meyer | As Ryan Budney pointed out above I should have found out whether or not only boundaryless manifolds are allowed instead of assuming that such "easy example" would be allowed. I therefore retract the first part of my first comment with apologies. | |
| Dec 12, 2009 at 0:38 | comment | added | Jonas Meyer | @sgots, But I wonder if this can be modified to give examples where there is no isometric imbedding into a complete Riemannian manifold of the same dimension. | |
| Dec 12, 2009 at 0:33 | comment | added | Mariano Suárez-Álvarez | Is a humble connected component of $\{(x,y,z):x^2+y^2=z^2\}\setminus0$ with the induced metric from $\mathbb R^3$ also an example? | |
| Dec 12, 2009 at 0:32 | comment | added | Jonas Meyer | There are easy examples of Riemannian manifolds whose completions as metric spaces are not manifolds, but I don't think that is what is asked for. | |
| Dec 11, 2009 at 23:45 | history | answered | some guy on the street | CC BY-SA 2.5 |