Higher Singularities and the Twistor Fibration π: CP3 → S4

Bolton, J.; Woodward, L.M.

Abstract

We use the Klein correspondences to write down an explicit relationship between two holomorphic curves, namely the directrix curve and the twistor lift, associated to a superminimal map from a Riemann surface to the 4-sphere. We also explain how the singularities of the corresponding osculating curves are related and show that they occur at the branch points or the umbilics of the corresponding superminimal map.

Citation

Bolton, J., & Woodward, L. (2000). Higher Singularities and the Twistor Fibration π: CP3 → S4. Geometriae Dedicata, 80(1-3), 231-246. https://doi.org/10.1023/a%3A100525941

• Journal Article Type: Article
• Publication Date: 2000-05
• Journal: Geometriae Dedicata
• Print ISSN: 0046-5755
• Electronic ISSN: 1572-9168
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 80
• Issue: 1-3
• Pages: 231-246
• DOI: https://doi.org/10.1023/a%3A100525941