Abstract
We discuss several kinds of Willmore surfaces of flat normal bundle in this paper. First we show that every S-Willmore surface with flat normal bundle in Sn must be located in some S3 ⊂ Sn, from which we characterize the Clifford torus as the only non-equatorial homogeneous minimal surface in Sn with flat normal bundle, which improves a result of K. Yang. Then we derive that every Willmore two sphere with flat normal bundle in Sn is conformal to a minimal surface with embedded planer ends in R3. We also point out that for a class of Willmore tori, they have a flat normal bundle if and only if they are located in some S3. In the end, we show that a Willmore surface with flat normal bundle must locate in some S6.
Original language | English |
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Pages (from-to) | 3245-3255 |
Number of pages | 11 |
Journal | Proceedings of the American Mathematical Society |
Volume | 141 |
Issue number | 9 |
DOIs | |
State | Published - 2013 |
Externally published | Yes |
Keywords
- Clifford torus
- Flat normal bundle
- S-Willmore surfaces
- Willmore sphere
- Willmore surfaces