Dr John Bolton john.bolton@durham.ac.uk
Bank Teacher
In [2] we discussed almost complex curves in the nearly Kähler S6. These are surfaces with constant Kähler angle 0 or π and, as a consequence of this, are also minimal and have circular ellipse of curvature. We also considered minimal immersions with constant Kähler angle not equal to 0 or π, but with ellipse of curvature a circle. We showed that these are linearly full in a totally geodesic S5 in S6 and that (in the simply connected case) each belongs to the S1-family of horizontal lifts of a totally real (non-totally geodesic) minimal surface in CP2. Indeed, every element of such an S1-family has constant Kähler angle and in each family all constant Kähler angles occur. In particular, every minimal immersion with constant Kähler angle and ellipse of curvature a circle is obtained by rotating an almost complex curve which is linearly full in a totally geodesic S5.
Bolton, J., Vrancken, L., & Woodward, L. (1997). Totally real minimal surfaces with non-circular ellipse of curvature in the nearly Kähler S6. Journal of the London Mathematical Society, 56(3), 625-644. https://doi.org/10.1112/s0024610797005541
Journal Article Type | Article |
---|---|
Publication Date | 1997-12 |
Journal | Journal of the London Mathematical Society |
Print ISSN | 0024-6107 |
Electronic ISSN | 1469-7750 |
Publisher | Wiley |
Peer Reviewed | Peer Reviewed |
Volume | 56 |
Issue | 3 |
Pages | 625-644 |
DOI | https://doi.org/10.1112/s0024610797005541 |
Public URL | https://durham-repository.worktribe.com/output/1626451 |
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