Infinitesimally Bonnet bendable hypersurfaces

Início: 31/03/2023 17:00

Término: 31/03/2023 18:00

Palestrante: Ruy Tojeiro (ICMC-USP (São Carlos))

E-mail do Palestrante: tojeiro@icmc.usp.br

Resumo: The classical Bonnet problem is to classify all immersions $fcolon,M^{2}to{R}^3$ 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 $ngeq3$ was studied by Kokubu. In this talk we report on joint work with M. Jimenez, in which we investigate an infinitesimal version of Bonnet problem for hypersurfaces with dimension $ngeq3$ of any space form, namely, we classify the hypersurfaces $fcolon{M}^{n}to{Q}_c^{n+1}$, $ngeq3$, of any space form $Q_c^{n+1}$ of constant curvature $c$, for which there exists a (non-trivial) one-parameter family of immersions $f_{t}colon{M}^{n}to{Q}_c^{n+1}$, with $f_0=f$, whose induced metrics $g_t$ and mean curvature functions $H_t$ coincide ``up to the first order", that is, $partial/partialt{|}_{t=0}{g}_t=0=partial/partialt{|}_{t=0}{H}_t.$