Local equivalence of sacksteder and bourgain hypersurfaces

Document Type

Article

Publication Date

1-1-2001

Abstract

Finding examples of tangentially degenerate submanifolds (submanifolds with degenerate Gauss mappings) in an Euclidean space R4 that are noncylindrical and without singularities is an important problem of differential geometry. The first example of such a hypersurface was constructed by Sacksteder in 1960. In 1995 Wu published an example of a noncylindrical tangentially degenerate algebraic hypersurface in R4 whose Gauss mapping is of rank 2 and which is also without singularities. This example was constructed (but not published) by Bourgain. In this paper, the authors analyze Bourgain’s example, prove that, as was the case for the Sacksteder hypersurface, singular points of the Bourgain hypersurface are located in the hyperplane at infinity of the space R4, and these two hypersurfaces are locally equivalent. © 2001 by the University of Notre Dame. All rights reserved.

Identifier

0013173231 (Scopus)

Publication Title

Hokkaido Mathematical Journal

External Full Text Location

https://doi.org/10.14492/hokmj/1350912798

ISSN

03854035

First Page

661

Last Page

670

Issue

3

Volume

30

This document is currently not available here.

Share

COinS