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Pseudoholomorphic Curves on Nearly Kähler Manifolds

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Abstract

Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kähler manifold. We prove that any connected component of the moduli space of pseudoholomorphic curves on M is compact. This can be used to study pseudoholomorphic curves on a 6-dimensional sphere with the standard (G 2-invariant) almost complex structure.

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Authors and Affiliations

  1. Faculty of Mathematics, National Research University HSE, 7 Vavilova Str., Moscow, Russia

    Misha Verbitsky

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  1. Misha Verbitsky
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Correspondence to Misha Verbitsky.

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Communicated by N. A. Nekrasov

Partially supported by RFBR grants 12-01-00944-, 10-01-93113-NCNIL-a, and AG Laboratory NRI-HSE, RF government grant, ag. 11.G34.31.0023, now I am also supported by the Simons-IUM fellowship.

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Verbitsky, M. Pseudoholomorphic Curves on Nearly Kähler Manifolds. Commun. Math. Phys. 324, 173–177 (2013). https://doi.org/10.1007/s00220-013-1751-9

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  • DOI: https://doi.org/10.1007/s00220-013-1751-9

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