General connections on vector bundles
type: Item
instance of: scholarly article
title: General connections on vector bundles
zbMATH Open document ID: 0594.53030
author: Naoto Abe
published in: Kodai Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: Let \({\mathfrak X}(M)\) be the F(M)-module of vector fields on a manifold M and let P be an endomorphism of it. A general connection on M is a map \(D: {\mathfrak X}(M)\times {\mathfrak X}(M)\to {\mathfrak X}(M)\), \((X,Y)\to D_ XY\), which is biadditive and satisfies \(D_{fX}Y=fD_ XY\), \(D_ XfY=Xf\cdot PY+fD_ XY\), for every X,Y\(\in {\mathfrak X}(M)\). This notion was introduced and studied by T. Otsuki in several papers. Now the general connections are called Otsuki connections. In this paper Otsuki connections on vector bundles are defined and their fundamental properties are studied. The theory of jet bundles is used.
Mathematics Subject Classification ID: 53C05
zbMATH DE Number: 3955914
zbMATH Keywords: general connection
zbMATH Keywords: Otsuki connections
zbMATH Keywords: jet bundles
reviewed by: Mihai Anastasiei
MaRDI profile type: Publication
OpenAlex ID: W2095517569
cites work: Q5726232
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DOI: 10.2996/KMJ/1138037100
description: scientific article; zbMATH DE number 3955914