Author:
Coelho R.,Placini G.,Stelzig J.
Abstract
AbstractWe study almost complex structures with lower bounds on the rank of the Nijenhuis tensor. Namely, we show that they satisfy an h-principle. As a consequence, all parallelizable manifolds and all manifolds of dimension $$2n\ge 10$$
2
n
≥
10
(respectively $$\ge 6$$
≥
6
) admit a almost complex structure whose Nijenhuis tensor has maximal rank everywhere (resp. is nowhere trivial). For closed 4-manifolds, the existence of such structures is characterized in terms of topological invariants. Moreover, we show that the Dolbeault cohomology of non-integrable almost complex structures is often infinite dimensional (even on compact manifolds).
Funder
Ludwig-Maximilians-Universität München
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Mathematics
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