Constrained Willmore Tori in the 4--Sphere

Details Constrained Willmore Tori in the 4--Sphere Constrained Willmore Tori in the 4--Sphere

2008-03-05

arxiv.org/abs/0803.0633v1

Mathematics

Differential Geometry

Scientific paper

We prove that a constrained Willmore immersion of a 2-torus into the conformal 4-sphere is either of ``finite type'', that is, has a spectral curve of finite genus, or is of ``holomorphic type'' which means that it is super conformal or Euclidean minimal with planar ends. This implies that all constrained Willmore tori in the 4-sphere can be constructed rather explicitly by methods of complex algebraic geometry. The proof uses quaternionic holomorphic geometry in combination with integrable systems methods similar to those of Hitchin's approach to the study of harmonic tori in the 3-sphere.

Affiliated with

Also associated with

No associations

Rating

Constrained Willmore Tori in the 4--Sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Constrained Willmore Tori in the 4--Sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constrained Willmore Tori in the 4--Sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-160974