Sequences of minimal surfaces in $S^{2n+1}$

Abstract

Let $M$ be minimal surface immersed into odd-dimensional sphere $S^{2n+1}$. In <i>Equivariant minimal immersions of $S^2$ into $S^{2m}$</i> (1) Ejiri introduced a notion of higher order ellipses of curvature. In this paper, for surface $M$ whose first $(n-2)$ ellipses of curvature are circles we construct a sequence of minimal surfaces which satisfies same condition on ellipses of curvature and we investigate if and when such two surfaces are congruent via an orientation reversing isometry.