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

Rivière Tristan

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

Differential Geometry 2019-12-03 v1

Authors: Rivière Tristan

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.

Keywords

harmonic maps mapping theory

Cite

@article{arxiv.1912.00473,
  title  = {Harmonic Maps from $S^3$ into $S^2$ with low Morse Index},
  author = {Rivière Tristan},
  journal= {arXiv preprint arXiv:1912.00473},
  year   = {2019}
}

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