Natural connections on the bundle of Riemannian metrics

2005/07/04 by Roberto Ferreiro Perez, Roberto Ferreiro Pérez, Perez, Roberto Ferreiro +3
Mathematics · Physics and Astronomy · #53B21 #57R20 #58A20 #58D19 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A55 #Secondary 53B05 #math.DG #msc:53A55 #msc:53B05 #msc:53B21 #msc:57R20 #msc:58A20 #msc:58D19

paper · pdf · doi:10.48550/arxiv.math/0507075

arxiv created 2005/07/04 · openalex publication_date 2005/07/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let FM,M_M be the bundles of linear frames and Riemannian metrics of a manifold M, respectively. The existence of a unique DiffM-invariant connection form on J¹M_M×_MFM→ J¹M_M, which is Riemannian with respect to the universal metric on J¹M_M×_MTM, is proved. Aplications to the construction of universal Pontryagin and Euler forms, are given.

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