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

Year: 2019
Type: preprint
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.
DOI: 10.48550/arxiv.1912.00473
Institution: ETH Zurich
Language: English
Open Access status: green
OpenAlex ID: W2991379189
Cites: 5
Cited by: 1
Related to: 20