Curvature of differentiable Hilbert modules and Kasparov modules

In this paper we introduce the curvature of densely defined universal connections on Hilbert C⁎-modules relative to a spectral triple (or unbounded Kasparov module), obtaining well-defined operator. Fixing triple, find that modulo junk forms, only depends represented form connection. We refine our definition factorizations modules. Our recovers all data Riemannian submersion compact manifolds, viewed as KK-factorization.