Isometric deformations of minimal surfaces in $S^{4}$

Theodoros Vlachos

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arXiv · 1202.6503

Isometric deformations of minimal surfaces in $S^{4}$

Theodoros Vlachos

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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.

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BibTeX RIS

Theodoros Vlachos. 2012-02-29. Isometric deformations of minimal surfaces in $S^{4}$. https://arxiv.org/abs/1202.6503

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