Isometric deformations of minimal surfaces in $S^4$

Abstract

We consider the isometric deformation problem for oriented non simply connected immersed minimal surfaces $f:M\to S^4$. We prove that the space of all isometric minimal immersions of $M$ into $S^4$ with the same normal curvature function is, within congruences, either finite or a circle. Furthermore, we show that for any compact immersed minimal surface in $S^4$ with nontrivial normal bundle there are at most finitely many noncongruent immersed minimal surfaces in $S^4$ isometric to it with the same normal curvature function.

References in corpus (1)

• The number of constant mean curvature isometric immersions of a surface