On maximal mobility of linearly connected spaces \(L_n\)
type: Item
instance of: scholarly article
title: On maximal mobility of linearly connected spaces \(L_n\)
zbMATH Open document ID: 0939.53009
DOI: 10.1007/BF02465557
author: A. P. Urbonas
published in: Lithuanian Mathematical Journal
publication date: 1999-04-27T00:00:00Z
review text: Let \(L\) be the space of linear elements \((x,l)\), where \(x=(x^1, \dots, x^n)\) and \(l=(l^1, \dots, l^n)\) subjected to the change of variables \(\overline x^i=f^i(x)\), \(\overline l^k=\sum f_s^kl^s\) (abbreviating \(f^i_k= \partial f^i/ \partial x^k)\). The space \(L\) is equiped with linear connections \(\Gamma=(\Gamma^1_1, \dots, \Gamma^n_n)\) which are homogeneous of order one with respect to the coordinates \(l^1,\dots,l^n\), and subjected to the transformation rule \(\Gamma^i_j(\overline x,\overline l)=\sum f^i_kg^r_j \Gamma^k_r (x,l)-\sum f^i_{ks}g^k_j l^s\) where \(x^k=g^k (\overline x)\) is the inversion. The author deals with infinitesimal symmetries \(x=x+v(x)\delta t\) satisfying the Lie derivative condition \(L_v\Gamma=0\) which is made more explicit in terms of the covariant derivatives and the curvature tensor. He is interested in connections which admit the largest possible symmetry groups.
Mathematics Subject Classification ID: 53B05
zbMATH DE Number: 1262946
zbMATH Keywords: linear connection
zbMATH Keywords: Lie symmetries
zbMATH Keywords: infinitesimal symmetries
reviewed by: Jan Chrastina
MaRDI profile type: Publication
cites work: The theory of sprays and Finsler spaces with applications in physics and biology
description: scientific article; zbMATH DE number 1262946