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Durham University

Department of Mathematical Sciences

Staff

Publication details for Dr John Bolton

Bolton, J., Vrancken, L. & Woodward, L.M. (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.

Author(s) from Durham

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.