Einstein submanifolds with parallel mean curvature into ${\mathbb{S}}^n\times \mathbb{R}$

We prove that Einstein submanifolds in ${\mathbb{S}}^n\times \mathbb{R}$ with flat normal bundle and parallel mean curvature are warped product of isometric immersions. Key words: Einstein submanifolds, Parallel mean curvature, Flat normal bundle.