Published Paper
Inserted: 8 nov 2016
Last Updated: 17 nov 2017
Journal: Differ. Geom. Appl.
Volume: 30
Number: 5
Pages: 530-547
Year: 2012
Doi: 10.1016/j.difgeo.2012.07.003
Abstract:
In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups made up of the classes admitting invariant, respectively anti-invariant, representatives with respect to the almost D-complex structure, miming the theory introduced by T.-J. Li and W. Zhang in T.-J. Li, W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom. 17 (2009), no. 4, 651-684 for almost complex manifolds. In particular, we prove that, on a 4-dimensional D-complex nilmanifold, such subgroups provide a decomposition at the level of the real second de Rham cohomology group. Moreover, we study deformations of D-complex structures, showing in particular that admitting D-Kaehler structures is not a stable property under small deformations.