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
[Copf ]P2. 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.