Transverse $J$-holomorphic curves in nearly K\"ahler $\mathbb{CP}^3$

Benjamin Aslan

Transverse $J$-holomorphic curves in nearly K\"ahler $\mathbb{CP}^3$

Differential Geometry 2021-01-12 v1

Authors: Benjamin Aslan

Abstract

$J$ -holomorphic curves in nearly K\"ahler $\mathbb{CP}^3$ are related to minimal surfaces in $S^4$ as well as associative submanifolds in $\Lambda^2_-(S^4)$ . We introduce the class of transverse $J$ -holomorphic curves and establish a Bonnet-type theorem for them. We classify flat tori in $S^4$ and construct moment-type maps from $\mathbb{CP}^3$ to relate them to the theory of $\mathrm{U}(1)$ -invariant minimal surfaces on $S^4$ .

Keywords

j-holomorphic curves nearly kahler manifolds minimal surfaces associative submanifolds bonnet theorem flat tori moment maps

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@article{arxiv.2101.03845,
  title  = {Transverse $J$-holomorphic curves in nearly K\"ahler $\mathbb{CP}^3$},
  author = {Benjamin Aslan},
  journal= {arXiv preprint arXiv:2101.03845},
  year   = {2021}
}

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31 pages, 4 figures

Transverse $J$-holomorphic curves in nearly K\"ahler $\mathbb{CP}^3$

Abstract

Keywords

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