GEOMETRY FROM THE SPECTRAL POINT-OF-VIEW

In this Letter, we develop geometry from a spectral point of view, the geometric data being encoded by a triple (A, H, D) of an algebra A re presented in a Hilbert space H with selfadjoint operator D. This point of view is dictated by the general framework of noncommutative geomet ry and allows us to use geometric ideas in many situations beyond Riem annian geometry.