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Totally real minimal surfaces with non-circular ellipse of curvature in the nearly Kähler S6

Bolton, J.; Vrancken, L.; Woodward, L.M.

Authors

L. Vrancken

L.M. Woodward



Abstract

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.

Citation

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