In this note, we deal with compact generalized (λ, n + m)-Einstein manifolds with nonempty boundary. More precisely, we extend some known results about compact static manifolds for (λ, n + m)-Einstein manifolds, giving topological classifications for its boundary. As a consequence, we obtain some characterizations of the round hemispheres.

中文翻译：

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广义（λ，n + m）-爱因斯坦流形的边界拓扑和刚度结果

在本说明中，我们处理具有非空边界的紧凑广义（λ，n  +  m）-爱因斯坦流形。更准确地说，我们扩展了关于（λ，n  +  m）-爱因斯坦流形的紧凑静态流形的一些已知结果，并为其边界给出了拓扑分类。结果，我们获得了圆形半球的一些特征。