%0 Journal Article
%T Isometric deformations of minimal surfaces in $S^{4}$
%A Theodoros Vlachos
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1202.6503v1