Differentiability of projective transformations in dimension 2
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Julius Lang
Abstract
It is proven by elementary methods that in dimension 2, every locally injective continuous map, sending the curves of a Ck-spray to curves of another Ck-spray as oriented point sets, is a Ck-diffeomorphism. This extends the result [1] for dimension three and higher from 1965.
Communicated by: T. Leistner
Acknowledgements
The problem appeared in discussions between Thomas Schneider, Markus Stroppel and Vladimir Matveev, whom I thank for posing it to me.
References
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Articles in the same Issue
- Frontmatter
- Topology of tropical moduli of weighted stable curves
- Classification of slant surfaces in 𝕊3 × ℝ
- New dense superball packings in three dimensions
- Explicit computation of some families of Hurwitz numbers, II
- An extension theorem for non-compact split embedded Riemannian symmetric spaces and an application to their universal property
- Moduli of stable sheaves supported on curves of genus three contained in a quadric surface
- Exceptional points for finitely generated Fuchsian groups of the first kind
- Tropical superelliptic curves
- Differentiability of projective transformations in dimension 2
- On pseudo-Einstein real hypersurfaces
- On the moduli spaces of singular principal bundles on stable curves
- Three-dimensional connected groups of automorphisms of toroidal circle planes
