Higher order differential lift equations over manifolds
type: Item
instance of: scholarly article
title: Higher order differential lift equations over manifolds
zbMATH Open document ID: 0889.58008
DOI: 10.1007/BF02435930
author: R. Greg Pond
published in: International Journal of Theoretical Physics
publication date: 1998-06-08T00:00:00Z
review text: This paper is of a technical nature. It studies two types of tangential resolutions for a differentiable manifold \(M\) modeled on a Banach space (real or complex), namely the full tangential resolution \((T^k(M), \pi_k)_{k \geq 0}\) of iterated tangent bundles and a restricted tangential resolution suggested by \textit{R. H. Bowman} [Tensor, New Ser. 21, 139-150, 261-264 (1970; Zbl 0179.27202, Zbl 0192.59102)]. In an earlier paper, the present author [\textit{R. Greg Pond}, Int. J. Theor. Phys. 36, No. 3, 715-741 (1997; Zbl 0873.58002)] has demonstrated that the full tangential resolution context is not the appropriate framework for the consideration of higher order differential lift equations defined by vector fields. In the present paper he shows, among other things, that every differential lift equation formulated in the full tangential resolution context can be formulated and fully treated in the (simpler) Bowman context.
Mathematics Subject Classification ID: 58A30
Mathematics Subject Classification ID: 58B99
zbMATH DE Number: 1066058
zbMATH Keywords: higher order differential lift equations
zbMATH Keywords: tangential resolution
reviewed by: Vagn Lundsgaard Hansen
MaRDI profile type: Publication
cites work: Q3277071
cites work: Q5560124
cites work: Q5570080
cites work: Higher order analogues of classical groups
cites work: Lift order problems for ordinary differential equations on manifolds
full work available at URL: https://doi.org/10.1007/bf02435930
OpenAlex ID: W2072038612
description: scientific article; zbMATH DE number 1066058