Natural connections given by general linear and classical connections

2004/10/21 by Josef Janyška, Janyška, Josef
Computer Science · Mathematics · #53C05 #58A20 #58A32 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #Polynomial and algebraic computation #math.DG #msc:53C05 #msc:58A20 #msc:58A32

paper · pdf · doi:10.48550/arxiv.math/0410461

arxiv created 2004/10/21 · openalex publication_date 2004/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We assume a vector bundle p: E→ M with a general linear connection K and a classical linear connection \Lam on M. We prove that all classical linear connections on the total space E naturally given by (\Lam, K) form a 15-parameter family. Further we prove that all connections on J¹ E naturally given by (\Lam, K) form a 14-parameter family. Both families of connections are described geometrically.

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