On the geometric structure of hypersurfaces of conullity two in Euclidean space. (English) Zbl 1119.53006

Ganchev, Georgi; Milousheva, Velichka

Mladenov, Ivaïlo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9–14, 2006. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-37-0/pbk). 169-183 (2007).

Summary: We introduce the notion of a semi-developable surface of codimension two as a generalization of the notion of a developable surface of codimension two. We give a characterization of the developable and semi-developable surfaces in terms of their second fundamental forms. We prove that any hypersurface of conullity two in Euclidean space is locally a foliation of developable or semi-developable surfaces of codimension two.
For the entire collection see [Zbl 1108.53003].

MSC:

53A07

Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces

Keywords:

semi-developable; second fundamental forms