Symmetries of almost complex structures and pseudoholomorphic foliations

Understand

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 briefly discuss the higher dimensions.