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Symmetries of almost complex structures and pseudoholomorphic foliations

Boris Kruglikov

Institute of Mathematics and Statistics, University of Tromsø, Tromsø 90-37, Norway

https://doi.org/10.1142/S0129167X14500797Cited by:3 (Source: Crossref)

Abstract

Contrary to complex structures, a generic almost complex structure J has no local symmetries. We give a criterion for finite-dimensionality of the pseudogroup G of local symmetries for a given almost complex structure J. It will be indicated that a large symmetry pseudogroup (infinite-dimensional) is a signature of some integrable structure, like a pseudoholomorphic foliation. We classify the sub-maximal (from the viewpoint of the size of G) symmetric structures J. Almost complex structures in dimensions 4 and 6 are discussed in greater details in this paper.

Keywords:

AMSC: 32Q60, 53C15, 53A55, 22E65

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