Cohomology of D-complex manifolds

详细信息    查看全文

• 作者：Daniele Angella ; Federico Alberto Rossi
• 关键词：53C15 ; 57T15 ; 32G07
• 刊名：Differential Geometry and its Applications
• 出版年：2012
• 出版时间：October, 2012
• 年：2012
• 卷：30
• 期：5
• 页码：530-547
• 全文大小：267 K

文摘

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 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-K?hler structures is not a stable property under small deformations.