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Compact Einstein-type manifolds with parallel Ricci tensor

Published 4 Mar 2024 in math.DG | (2403.02447v1)

Abstract: In this paper, we deduce a Bochner-type identity for compact gradient Einstein-type manifolds with boundary. As consequence, we are able to show a rigidity result for Einstein-type manifolds assuming the parallel Ricci curvature condition. Moreover, we provide a condition on the norm of the gradient of the potential function in order to classify such structures.

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