Arnold's seminar
March 5, 2002

B.Kruglikov (University of Tromso, Norway)
"Are there pseudoholomorphic submanifolds of complex dimensions
greater than one?"
  
The negative answer to this question (provided that the almost complex
structure is generic) is clear to all working with pseudoholomorphic curves.
However there is a lack of argumentation. It will be presented in the talk.
We give several approaches to the problem. First naive is connected with
investigation of integral Grassmannians produced by the Nijenhuis tensor.
The second is to study obstructions to solvability of the corresponding PDE
system. The last method to consider invariants also solves the problem.