CONNECTIONS ON CENTRAL BIMODULES IN NONCOMMUTATIVE DIFFERENTIAL GEOMETRY

We define and study the theory of derivation-based connections on a re cently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theo ry contains, in particular, a noncommutative generalization of linear connections. We also discuss the different noncommutative versions of differential farms based on derivations. Then we investigate reality c onditions and a noncommutative generalization of pseudo-riemannian str uctures.