Let M^n(n ≥ 4) be an oriented closed submanifold with parallel mean curvature in an(n + p)-dimensional locally symmetric Riemannian manifold N^(n+p). We prove that if the sectional curvature of N is positively pinched in [δ, 1], and the Ricci curvature of M satisfies a pinching condition, then M is either a totally umbilical submanifold, or δ = 1, and N is of constant curvature. This result generalizes the geometric rigidity theorem due to Xu and Gu[15].
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