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- Title
Infinitesimally Bonnet Bendable Hypersurfaces.
- Authors
Jimenez, M. I.; Tojeiro, R.
- Abstract
The classical Bonnet problem is to classify all immersions f : M 2 → R 3 into Euclidean three-space that are not determined, up to a rigid motion, by their induced metric and mean curvature function. The natural extension of Bonnet problem for Euclidean hypersurfaces of dimension n ≥ 3 was studied by Kokubu (Tôhoku Math J 44:433–442, 1992). In this article, we investigate an infinitesimal version of Bonnet problem for hypersurfaces with dimension n ≥ 3 of any space form, namely, we classify the hypersurfaces f : M n → Q c n + 1 , n ≥ 3 , of any space form Q c n + 1 of constant curvature c, for which there exists a (non-trivial) one-parameter family of immersions f t : M n → Q c n + 1 , with f 0 = f , whose induced metrics g t and mean curvature functions H t coincide "up to the first order," that is, ∂ / ∂ t | t = 0 g t = 0 = ∂ / ∂ t | t = 0 H t.
- Subjects
CALCULUS; MATHEMATICS; ISOTHERMIC surfaces (Mathematics); DIFFERENTIAL geometry; EUCLIDEAN geometry
- Publication
Journal of Geometric Analysis, 2023, Vol 33, Issue 5, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-022-01181-x