Small Nijenhuis tensors on compact almost complex manifolds with no complex structure

Abstract: I will present several examples of compact almost complex manifolds with a $1$-parameter family of almost complex structures having arbitrarily small Nijenhuis tensors in the $C^0$-norm. The $4$-dimensional examples possess no complex structure, while the $6$-dimensional examples do not possess left invariant complex structures, and whether they possess complex structures appears to be unknown. This is joint work with Luis Fernandez and Tobias Shin.

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

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