Generalized coKahler geometry and an application to generalized Kahler structures

In this paper, we propose a generalization of classical coKahler 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 M-1 x M-2 of generalized contact metric manifolds (M-i, Phi(i), E-+/-,E-i, G(i)), i = 1, 2, where M-1 x M-2 is endowed with the product (twisted) generalized complex structure induced from Phi(1) and Phi(2), is (twisted) generalized Kahler if and only if (M-i, Phi(i), E-+/-,E-i, G(i)), i = 1, 2 are (twisted) generalized coKahler structures. As an application of our theorem we construct new examples of twisted generalized Miller structures on manifolds that do not admit a classical Kahler structure and we give examples of twisted generalized coKahler structures on manifolds which do not admit a classical coKahler structure. (C) 2015 Elsevier B.V. All rights reserved.