We will report on joint works with Paola Frediani, Juan Carlos Naranjo and Gian Pietro Pirola. We study the second fundamental form of the Siegel metric in A_5 restricted to the moduli space of the intermediate jacobians cubic threefolds and the second fundamental form in A_9 restricted to the moduli of the the intermediate jacobians of (2,2) threefolds in P^2xP^2 . In both case there is a natural composition with a multiplication map. For cubic threefold this composition results to be zero, while for (2,2) threefolds it gives a not zero holomorphic section of a bundle.