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Non-existence of higher-dimensional pseudoholomorphic submanifolds

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Abstract.

 In this paper we prove that only pseudoholomorphic curves appear as J-invariant submanifolds of generic almost complex manifolds (M,J). We also prove there exist no non-trivial automorphisms or submersions of such manifolds. On the other hand we show that abundance of 1-jets of PH-submanifolds, automorphisms or submersions implies integrability of the almost complex structure.

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Authors and Affiliations

  1. Department of Math. and Stat., University of Tromsoe, Norway and Mathem. Modelling Chair, Moscow Baumann State Technological University, Russia. e-mail: kruglikov@math.uit.no, , , , , , RU

    Boris S. Kruglikov

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  1. Boris S. Kruglikov
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Received: 19 April 2002 / Revised version: 10 October 2002 Published online: 14 February 2003

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Kruglikov, B. Non-existence of higher-dimensional pseudoholomorphic submanifolds. manuscripta math. 111, 51–69 (2003). https://doi.org/10.1007/s00229-002-0352-2

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  • DOI: https://doi.org/10.1007/s00229-002-0352-2

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