2017/05/31 by Fernando Etayo, Etayo, Fernando, Rafael Santamaría +1
Mathematics · Physics and Astronomy · #53C05 #53C07 #53C15 #53C50 #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.1705.11135
openalex publication_date 2017/05/31 · openalex created_date 2017/06/05 · openalex updated_date 2026/07/28
A (J2=± 1)-metric manifold has an almost complex or almost product structure J and a compatible metric g. We show that there exists a canonical involution in the set of connections on such a manifold, which allows to define a projection over the set of connections adapted to J. This projection sends the Levi Civita connection onto the first canonical connection. In the almost Hermitian case, it also sends the ∇- connection onto the Chern connection, thus applying the line of metric connections defined by ∇ - and the Levi Civita connections onto the line of canonical connections. Besides, it moves metric connections onto metric connections.