Singular genuine rigidity

  • Luis A. Florit

    Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
  • Felippe Guimarães

    Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
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Abstract

We extend the concept of genuine rigidity of submanifolds by allowing mild singularities, mainly to obtain newglobal 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 -dimensional submanifold of is singularly genuinely rigid in , for any . 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.

Cite this article

Luis A. Florit, Felippe Guimarães, Singular genuine rigidity. Comment. Math. Helv. 95 (2020), no. 2, pp. 279–299

DOI 10.4171/CMH/488