Black hole entropy and topological strings on generalized CY manifolds

The H. Ooguri, A. Strominger and C. Vafa conjecture Z(BH) = vertical bar Z(top)vertical bar(2) is extended for the topological strings on generalized CY manifolds. It is argued that the classical black hole entropy is given by the generalized Hitchin functional, which defines by critical points a generalized complex structure on X. This geometry differs from an ordinary geometry if b(1)( X) not equal 0. In a critical point the generalized Hitchin functional equals to Legendre transform of the free energy of generalized topological string. The examples of T-6 and T-2 x K3 are considered in details.