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Results tagged with dg.differential-geometry
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user 36502
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
9
votes
Accepted
Lorentzian metrics on the torus up to continuos deformations
Yes those are already all different metrics. Since the tangent bundle of the 2-torus $\mathbb{T}^2$ is trivial you have a correspondence between the set of homotopy classes of maps $\mathbb{T}^2\to\ma …
- 523
2
votes
Spin structures and divisibility of cohomology classes
I think your last sentence/question is not well posed. It is well known that there are flat manifolds admitting plenty of non-flat vector bundles. E.g. see J. Smillie, "Flat manifolds with non-zero Eu …
- 523
1
vote
Lorentzian metrics on a disk up to conformal equivalence
It seems the answer is no. See the paper "An Analogue of the Riemann Mapping Theorem for Lorentz Metrics" by R. S. Kulkarni, Proc. R. Soc. Lond. A 9 September 1985 vol. 401 no. 1820 117-130.
- 523
1
vote
Are there examples of compact infinite dimensional manifolds?
Yes. Compact Hilbert cube manifolds, for instance.
- 523