General connections on vector bundles
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.
scientific article; zbMATH DE number 3955914
scientific article