In this paper we obtain a simple upper bound for the infimum of the Riccicurvatures of a complete Riemannian manifold with nonzero injectivity radiusi(M) depending only on of the i(M). In case of rigidity the Riemannian manifoldmust be an Euclidean sphere(Euclidean space) conform the injectivity radius befinite(infinite). Furthermore with the additional assumption that the secondderivative of the Ricci tensor is null we prove that the same upper bound forthe infimum of the Ricci curvatures holds for the supremum of the Riccicurvatures and $M^n$ has, in fact, parallel Ricci tensor.
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机译：在本文中，我们获得了一个完整的黎曼流形的Riccicurvatures的极小值的上界，其中，Riecimann流形的非零注入半径仅取决于i（M）。在刚度的情况下，黎曼流形必须是一个欧几里得球（欧几里得空间），其射入半径必须是确定的（无限大）。此外，还假设Ricci张量的二阶导数为零，我们证明Ricci曲率的最小值的相同上限适用于Ricci曲率的极值，而$ M ^ n $实际上具有平行的Ricci张量。
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