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Results tagged with dg.differential-geometry
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user 68927
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
2
votes
1
answer
297
views
Extrinsic horizontal path lifting
As a follow up question to my previous question about the orthonormal frame bundle, I would like to understand a simple example explicitly.
Let $\mathbb{S}^2$ be written extrinsically as $$\mathbb{S …
- 396
1
vote
Extrinsic horizontal path lifting
So I think I have an answer, but instead of using the ODE in Step 3, it uses a simpler equation that implies it: $$ \dot{w} = \tilde{\gamma}^{-1}\dot{\gamma}\,. $$
Here $w:[0,1]\to\mathbb{R}^2$ is a …
- 396
3
votes
1
answer
451
views
Orthonormal frame bundles on a manifold
Let $(\mathcal{M},g)$ be a torsion free compact Riemannian manifold of dimension $n$. Hence from the metric we know there is an associated horizontal sub-bundle $H_u F \mathcal{M}$ of the orthonormal …
- 396