Almost complex manifolds with small Nijenhuis tensor

Abstract

We give several explicit examples of compact manifolds with a 1-parameter family of almost complex structures having arbitrarily small Nijenhuis tensor in the C0-norm. The 4-dimensional examples possess no complex structure, whereas the 6-dimensional example does not possess a left invariant complex structure, and whether it possesses a complex structure appears to be unknown.

Keywords

• almost complex manifold
• nijenhuis tensor
• 32q60
• 53c15