A note on the coincidence of the projective and conformal Weyl tensors

2013/01/23 by Christian Lübbe, Lübbe, Christian
Mathematics · Physics and Astronomy · #53A20 #53A30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1301.5659

openalex publication_date 2013/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article examines the coincidence of the projective and conformal Weyl tensors associated to a given connection D. The connection may be a general Weyl connection associated to a conformal class of metrics [g]. The main result for n>3 is that the Weyl tensors coincide iff D is the Levi-Civita connection of an Einstein metric.

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