Isometric immersions of contact Riemannian manifolds in real space forms

First, we define some contact Riemannian invariants for almost contact metric manifolds analogues to those invariants introduced in [5, 6]. We then establish sharp inequalities between these contact Riemannian invariants and the squared mean curvature for almost contact Riemannian manifolds in a real space form. We also investigate almost contact Riemannian submanifolds which verify the equality case of the inequalities. Examples of contact Riemannian submanifolds satisfying the equality case are provided as well.