Sequences of Willmore surfaces

Details Sequences of Willmore surfaces Sequences of Willmore surfaces

2006-10-21

arxiv.org/abs/math/0610648v1

Math. Z. (2008) 259: 113-122

Mathematics

Differential Geometry

10 pages

Scientific paper

10.1007/s00209-007-0214-4

In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the twistor projection of a holomorphic curve into complex projective space or the inversion of a minimal surface with planar ends in 4-space. These results give a unified explanation of previous work on the characterization of Willmore spheres and Willmore tori with non-trivial normal bundles by various authors.

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