Natural transformations of symmetric affine connections on manifolds to metrics on linear frame bundles: A classification
type: Item
instance of: scholarly article
title: Natural transformations of symmetric affine connections on manifolds to metrics on linear frame bundles: A classification
zbMATH Open document ID: 0639.53022
DOI: 10.1007/BF01636931
author: Masami Sekizawa
published in: Monatshefte für Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178378
review text: We apply concepts and methods due to \textit{D. Krupka} [Arch. Math., Brno 14, 207-214 (1978; Zbl 0428.58002)] to find all second order natural transformations of symmetric affine connections on manifolds into metrics on linear frame bundles. The complete family of naturally resulting metrics (to a fixed symmetric affine connection) is a real vector space generated by some generalization of two ``classical'' liftings.
Mathematics Subject Classification ID: 53B05
zbMATH DE Number: 4042740
zbMATH Keywords: natural transformations
zbMATH Keywords: affine connections
zbMATH Keywords: frame bundles
MaRDI profile type: Publication
cites work: Lifts of tensor fields to the frame bundle
cites work: On the curvature of the induced Riemannian metric on the frame bundle of a Riemannian manifold
cites work: Q5731354
cites work: Q3865173
cites work: Q5658749
cites work: On the differential geometry of frame bundles of Riemannian manifolds.
cites work: On the differential geometry of frame bundles
cites work: Recurrent Tensors on a Linearly Connected Differentiable Manifold
description: scientific article; zbMATH DE number 4042740