Submanifolds with degenerate Gauss mappings in spheres (Q2752892)

Let \(M\) be a \(l\)-dimensional submanifold of the sphere \(S^{n}\) and denote by \( \gamma \) its Gauss map and \( r=\text{ max}_{p \in M} \text{ rank}_{p} \gamma \). The problems the authors are concerning with are the following:NEWLINENEWLINENEWLINEa) Is the inequality \(r<\) Ferus number \(F(l)\) best possible for the implication \(r=0\)? NEWLINENEWLINENEWLINEb) Do there exist tangentially degenerate compact submanifolds of \(S^{n}\) with \(r=F(l)\)? NEWLINENEWLINENEWLINEc) The submanifolds of b) can be classified? NEWLINENEWLINENEWLINEThis is a survey note of the authors' work ''Submanifolds with degenerate Gauss mapping in the sphere'', submitted for publication.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00049].