2017/06/29 by Jimenez, Miguel Ibieta
#53A07 #53C40 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1706.09545
A local description of the non-flat infinitesimally bendable Euclidean hypersurfaces was recently given by Dajczer and Vlachos \citeDaVl. From their classification, it follows that there is an abundance of infinitesimally bendable hypersurfaces that are not isometrically bendable. In this paper we consider the case of complete hypersurfaces f\colon Mn→ℝn+1, n≥ 4. If there is no open subset where f is either totally geodesic or a cylinder over an unbounded hypersurface of ℝ4, we prove that f is infinitesimally bendable only along ruled strips. In particular, if the hypersurface is simply connected, this implies that any infinitesimal bending of f is the variational field of an isometric bending.