Quantization of Locally Symmetric Kähler Manifolds

Abstract

We introduce noncommutative deformations of locally symmetric Kähler manifolds. A Kähler manifold $M$ is said to be a locally symmetric Kähler manifold if the covariant derivative of the curvature tensor is vanishing . An algebraic derivation process to construct a locally symmetric Kähler manifold is given. As examples, star products for noncommutative Riemann surfaces and noncommutative $\mathbb {CP}^N$ are constructed.