2018/03/16 by Luis A. Florit, Florit, Luis A., Felippe Guimarães +1
Mathematics · #53B25 #53C40 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53B25 #msc:53C40
paper · pdf · doi:10.48550/arxiv.1803.06395
18 pages, accepted for publication in Comment. Math. Helv
arxiv created 2018/12/08 · arxiv updated 2018/12/11
We extend the concept of genuine rigidity of submanifolds by allowing mild singularities, mainly to obtain new global rigidity results and unify the known ones. As one of the consequences, we simultaneously extend and unify Sacksteder and Dajczer-Gromoll theorems by showing that any compact n-dimensional submanifold of \mathbb Rn+p is singularly genuinely rigid in \mathbb Rn+q, for any q < min\5,n\ - p. Unexpectedly, the singular theory becomes much simpler and natural than the regular one, even though all technical codimension assumptions, needed in the regular case, are removed.