Isometric deformations of isotropic surfaces

Abstract

It was shown by Ramanathan (Manuscripta Math 60:417–422, 1988) that any compact oriented minimal surface in the three-dimensional round sphere admits at most a finite set of pairwise noncongruent minimal isometric immersions. In this paper, we extend this result to isotropic surfaces in spheres of higher dimension. The case of isotropic surfaces other than compact in space forms is also addressed.