Isometric deformations of pseudoholomorphic curves in the nearly K{ä}hler sphere ${\mathbb{S}}^6$

The aim of the paper is to investigate the rigidity and the deformability of pseudoholomorphic curves in the nearly K{ä}hler sphere ${\mathbb{S}}^6,$ among minimal surfaces in spheres. Under various assumptions we describe the moduli space of all noncongruent minimal surfaces $f\text{\hspace{0.17em}⁣}:M\to {\mathbb{S}}^n$ that are isometric to a pseudoholomorphic curve in ${\mathbb{S}}^6\mathrm{.}$ Moreover, we prove a Schur type theorem (see \cite[p. 36]{Chnew}) for minimal surfaces in spheres.