Abstract
We provide an elementary proof of the fact that the space of all isometric minimal immersions $f:M\to\mathbb{S}^{4}$ of a 2-dimensional Riemannian manifold $M$ into $\mathbb{S}^{4}$ with the same normal curvature is, up to congruence, either finite or a circle. Furthermore, we show that if $M$ is compact and the Euler number of the normal bundle of $f$ is nonzero, then there exist at most finitely many noncongruent isometric minimal immersions of $M$ into $\mathbb{S}^{4}$ with the same normal curvature.
Citation
Theodoros Vlachos. "Isometric deformations of minimal surfaces in $\mathbb{S}^{4}$." Illinois J. Math. 58 (2) 369 - 380, Summer 2014. https://doi.org/10.1215/ijm/1436275488
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