Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666058 | Advances in Mathematics | 2013 | 25 Pages |
Abstract
In this paper, we study degenerate CR embeddings f of a strictly pseudoconvex hypersurface MâCn+1 into a sphere S in a higher dimensional complex space CN+1. The degeneracy of the mapping f will be characterized in terms of the ranks of the CR second fundamental form and its covariant derivatives. In 2004, the author, together with X. Huang and D. Zaitsev, established a rigidity result for CR embeddings f into spheres in low codimensions. A key step in the proof of this result was to show that degenerate mappings are necessarily contained in a complex plane section of the target sphere (partial rigidity). In the 2004 paper, it was shown that if the total rank d of the second fundamental form and all of its covariant derivatives is
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Peter Ebenfelt,