Envelopes and osculates of Willmore surfaces

• Autores: K. Leschke, Franz Pedit
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 75, Nº 1, 2007, págs. 199-212
• Idioma: inglés
• DOI: 10.1112/jlms/jdl003
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• Resumen

  • 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.