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.

Cohomology of D-complex manifolds / Angella, Daniele; Rossi, Federico Alberto. - In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. - ISSN 0926-2245. - STAMPA. - 30:(2012), pp. 530-547. [10.1016/j.difgeo.2012.07.003]

Cohomology of D-complex manifolds

ANGELLA, DANIELE;
2012

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.
2012
30
530
547
Angella, Daniele; Rossi, Federico Alberto
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1009013
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