Symmetries of almost complex structures and pseudoholomorphic foliations

Details Symmetries of almost complex structures and pseudoholomorphic foliations Symmetries of almost complex structures and pseudoholomorphic foliations

2011-03-22

arxiv.org/abs/1103.4404v2

Mathematics

Differential Geometry

This version is an elaboration of the first one in the following: some results are improved, minor incoherences helped, genera

Scientific paper

Generically an almost complex structure has no symmetries at all, but there exist symmetric structures. In this paper we describe how to guarantee that the pseudogroup of local symmetries is small (finite-dimensional). It will be indicated that a large symmetry pseudogroup (infinite-dimensional) is a signature of some integrable structure, like a pseudoholomorphic foliation. We are mostly concerned with almost complex structures in dimensions 4 and 6, where we classify the sub-maximal symmetric structures, and we will briefly discuss the higher dimensions.

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