arXiv 1502.070462015-02math.DG

Generalized CoKähler Geometry and an Application to Generalized Kähler Structures

Ralph R. Gomez, Janet Talvacchia

备注：: Final print version. To appear in Journal of Geometry and Physics
DOI：: 10.1016/j.geomphys.2015.09.001

英文摘要：

In this paper we define the notion of a generalized coKähler structure and prove that the product $M_{1}\times M_{2}$ of generalized contact metric manifolds $(M_i, Φ_i,E_{\pm,i}, G_i)$, $ i=1, 2$, where $M_{1}\times M_{2}$ is endowed with the product generalized complex structure induced from $Φ_1$ and $Φ_2$, is generalized Kähler if and only if $(M_i, Φ_i, E_{\pm,i}, G_i) ,\ \ i=1,2$ are generalized coKähler structures. We also prove that products of generalized coKähler and generalized Kähler manifolds admit a generalized coKähler structure. We use these product constructions to give nontrivial examples of generalized coKähler structures. Finally, we show the analogs of these theorems hold in the setting of twisted generalized geometries. We use these theorems to construct new examples of twisted generalized Kähler structures on manifolds that do not admit a classical Kähler structure and we give examples of twisted generalized coKähler structures on manifolds which do not admit a classical coKähler structure.

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