We present some fine properties of immersions ℐ:M N between manifolds, with particular attention to the case of immersed curves c:S1 ℝn. We present new results, as well as known results but with quantitative statements (that may be useful in numerical applications) regarding tubular coordinates, neighborhoods of immersed and freely immersed curve, and local unique representations of nearby such curves, possibly "up to reparameterization."We present examples and counterexamples to support the significance of these results. Eventually, we provide a complete and detailed proof of a result first stated in a 1991-paper by Cervera, Mascaró, and Michor: the quotient of the freely immersed curves by the action of reparameterization is a smooth (infinite dimensional) manifold.
Neighborhoods and manifolds of immersed curves
Mennucci, Andrea Carlo Giuseppe
2021
Abstract
We present some fine properties of immersions ℐ:M N between manifolds, with particular attention to the case of immersed curves c:S1 ℝn. We present new results, as well as known results but with quantitative statements (that may be useful in numerical applications) regarding tubular coordinates, neighborhoods of immersed and freely immersed curve, and local unique representations of nearby such curves, possibly "up to reparameterization."We present examples and counterexamples to support the significance of these results. Eventually, we provide a complete and detailed proof of a result first stated in a 1991-paper by Cervera, Mascaró, and Michor: the quotient of the freely immersed curves by the action of reparameterization is a smooth (infinite dimensional) manifold.File | Dimensione | Formato | |
---|---|---|---|
neigh_manif_curves.pdf
accesso aperto
Tipologia:
Accepted version (post-print)
Licenza:
Creative Commons
Dimensione
427.01 kB
Formato
Adobe PDF
|
427.01 kB | Adobe PDF | |
11384_102259_ed.pdf
accesso aperto
Tipologia:
Published version
Licenza:
Creative Commons
Dimensione
1.8 MB
Formato
Adobe PDF
|
1.8 MB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.