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Positive Ricci curvature on fiber bundles with compact structure group

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Abstract This paper presents a direct and simple proof of a result concerning the existence of metrics of positive Ricci curvature on the total space of fiber bundles with compact… Click to show full abstract

Abstract This paper presents a direct and simple proof of a result concerning the existence of metrics of positive Ricci curvature on the total space of fiber bundles with compact structure groups. In particular, it generalizes and puts in a unified framework the results of Nash [12] and Poor [15]. With the intention of disseminating this result,we apply it to build new examples of manifolds with positive Ricci curvature, including bundles whose base consists of gradient shrinking Ricci solitons.

Keywords: compact structure; bundles compact; fiber bundles; positive ricci; ricci curvature

Journal Title: Advances in Geometry
Year Published: 2022

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