Envelopes and osculates of Willmore surfaces

Authors

K Leschke
F Pedit, University of Massachusetts - AmherstFollow

Publication Date

2007

Journal or Book Title

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

Abstract

We view conformal surfaces in the 4-sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new holomorphic curves in quaternionic projective space and thus new conformal surfaces. Applying these constructions to Willmore surfaces, we show that the osculating and enveloping curves of Willmore spheres remain Willmore.

Comments

This is the pre-published version harvested from arXiv. The published version is located at http://jlms.oxfordjournals.org/content/75/1/199.full

Pages

199-212

Volume

75

Recommended Citation

Leschke, K and Pedit, F, "Envelopes and osculates of Willmore surfaces" (2007). JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES. 758.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/758