Journal Of Geometry And Physics
In this paper, we propose a generalization of classical coKähler geometry from the point of view of generalized contact metric geometry. This allows us to generalize a theorem of Capursi (1984), Goldberg (1968) and show that the product M1×M2M1×M2 of generalized contact metric manifolds (Mi,Φi,E±,i,Gi)(Mi,Φi,E±,i,Gi), i=1,2i=1,2, where M1×M2M1×M2 is endowed with the product (twisted) generalized complex structure induced from Φ1Φ1 and Φ2Φ2, is (twisted) generalized Kähler if and only if View the MathML source(Mi,Φi,E±,i,Gi),i=1,2 are (twisted) generalized coKähler structures. As an application of our theorem we 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.
Ralph R. Gomez and Janet Talvacchia.
"Generalized CoKähler Geometry And An Application To Generalized Kähler Structures".
Journal Of Geometry And Physics.