Abstract: The compact submanifolds in quasi constant curvature Riemannian manifolds with Parallel Mean Curature Vector were studied. By using Stokes theorem, and some last results of algebra inequation, an integral inequality was obtained. The work makes the study of compact submanifolds in quasi constantcurvature Riemannian manifolds extend from the especial case to general case.

Key words: parallel mean curvature, Riemannian manifold, compact submanifold