Some canonical metrics \em via Aubin's local deformations

2022/06/22 by Giovanni Catino, Davide Dameno, Catino, Giovanni +3 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.2206.11016

openalex publication_date 2022/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, using special metric deformations introduced by Aubin, we construct Riemannian metrics satisfying non-vanishing conditions concerning the Weyl tensor, on every compact manifold. In particular, in dimension four, we show that there are no topological obstructions for the existence of metrics with non-vanishing Bach tensor.

Cited by

• Bach-pinched metrics on closed manifolds

Related

• Bach-pinched metrics on closed manifolds
• On the Existence of Certain Metrics with Non Parallel Ricci Tensor
• Four dimensional closed manifolds admit a weak harmonic Weyl metric
• On the set of metrics without local limiting Carleman weights
• Metrics of constant negative scalar-Weyl curvature