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Journal of the London Mathematical Society Advance Access originally published online on January 29, 2007
Journal of the London Mathematical Society 2007 75(1):199-212; doi:10.1112/jlms/jdl003
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© 2007 London Mathematical Society

Envelopes and osculates of Willmore surfaces

K. Leschke and F. Pedit

Department of Mathematics
University of Massachusetts
Amherst
MA 01003
USA
leschke{at}math.umass.edu
franz{at}math.umass.edu

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.

2000 Mathematics Subject Classification 53Axx, 53Cxx, 30Fxx.

The authors were partially supported by SFB288, and the first author was partially supported by NSF-grant DMS-9626804.

Received August 31, 2004; revised October 25, 2005; published online January 29, 2007.


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