Almost complex manifolds with small Nijenhuis tensor

2021/03/10 by Fernandez, Luis, Shin, Tobias, Wilson, Scott O.
#Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2103.06090

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 possesses a left invariant complex structure, and whether it possesses a complex structure appears to be unknown.

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