Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606214 | Differential Geometry and its Applications | 2012 | 18 Pages |
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 Li and Zhang (2009) in [20] 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-Kähler structures is not a stable property under small deformations.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Daniele Angella, Federico Alberto Rossi,