Natural transformations of vector fields on manifolds to vector fields on tangent bundles
type: Item
instance of: scholarly article
title: Natural transformations of vector fields on manifolds to vector fields on tangent bundles
zbMATH Open document ID: 0657.53009
author: Masami Sekizawa
published in: Tsukuba Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The main result of the paper is that all first order natural operators transforming every vector field on a manifold M into a vector field on its tangent bundle form a 3-parameter family linearly generated by the flow operator, the vertical lift and the Liouville vector field. [The reviewer has recently deduced that the same result holds under no assumption on the order of the operators, Ann. Global Anal. Geom. 6, 109- 117 (1988)]. The author also determines all second order natural transformations of a linear symmetric connection on M and a vector field on M into a vector field on TM.
Mathematics Subject Classification ID: 53A55
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 53B05
zbMATH DE Number: 4073869
zbMATH Keywords: first order natural operators
zbMATH Keywords: vector field
zbMATH Keywords: tangent bundle
zbMATH Keywords: flow operator
zbMATH Keywords: vertical lift
zbMATH Keywords: Liouville vector field
zbMATH Keywords: second order natural transformations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496160639
OpenAlex ID: W1554915267
DOI: 10.21099/TKBJM/1496160639
reviewed by: Ivan Kolář
description: scientific article; zbMATH DE number 4073869