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arXiv · 1912.00473

Harmonic Maps from $S^3$ into $S^2$ with low Morse Index

Rivière Tristan
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Abstract

We prove that any smooth harmonic map from $S^3$ into $S^2$ of Morse index less or equal than $4$ has to be an harmonic morphism, that is the successive composition of an isometry of $S^3$, the Hopf fibration and an holomorphic map from ${\mathbb C}P^1$ into itself.

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Rivière Tristan. 2019-12-01. Harmonic Maps from $S^3$ into $S^2$ with low Morse Index. https://arxiv.org/abs/1912.00473

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