Abstract: Quantum Heisenberg Manifolds were first defined by M. Rieffel in 1989 as example of quantization of Heisenberg Manifolds along a Poisson bracket.(A typical Heisenberg Manifold is the quotient of Heisenberg group by a uniform lattice).They are interesting for several reasons, one being just because they are tractable examples of noncommutative manifolds.This means that , like the related but simpler noncommutative tori, Q-Heisenberg manifolds provide a nice setting in which to explore noncommutative geometry.

In these series of talks I will explore the different features of the noncommutative geometry on Q-Heisenberg manifolds. We introduce a class of spectral triples on Q-Heisenberg manifold, we introduce the space of L^2 -forms and then we characterize torsion less/Unitary connections. In addition, for a concrete family of unitary connections we compute Ricci curvature and scalar curvature.