On some compact almost Kähler locally symmetric space

Abstract

In the framework of studying the integrability of almost Kähler manifolds, we prove that if a compact almost Kähler locally symmetric space M is a weakly ,∗-Einstein vnanifold with non-negative ,∗-scalar curvature, then M is a Kähler manifold.

Keywords

• Almost Kähler manifolds
• locally symmetric spaces and weakly ∗-Einstein manifolds.