Generalized CoKähler Geometry and an Application to Generalized Kähler Structures

Abstract

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 $(M_i,{\Phi }_i,E_{\pm ,i},G_i)$, $i=1,2$, where $M_1\times M_2$ is endowed with the product generalized complex structure induced from ${\Phi }_1$ and ${\Phi }_2$, is generalized Kähler if and only if $(M_i,{\Phi }_i,E_{\pm ,i},G_i),i=1,2$ 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.

Final print version. To appear in Journal of Geometry and Physics

References in corpus (3)

• Generalised Geometry for M-Theory
• Generalized complex geometry
• Linearizing Generalized Kahler Geometry

Cited by in corpus (4)

• An Abstract Morimoto Theorem for Generalized $F$-structures
• Generalised contact geometry as reduced generalised complex geometry
• On hypersurfaces of generalized Kähler manifolds
• Commuting Pairs of Generalized Contact Metric Structures