Publication details

 

Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case

Basic information
Original title:Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case
Authors:Josef Janyška, Martin Markl
Further information
Citation:JANYŠKA, Josef a Martin MARKL. Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case. Archivum Mathematicum, Brno: Masaryk University, 2012, roč. 48, č. 1, s. 61-80. ISSN 0044-8753. doi:10.5817/AM2012-1-61.Export BibTeX
@article{980449,
author = {Janyška, Josef and Markl, Martin},
article_location = {Brno},
article_number = {1},
doi = {http://dx.doi.org/10.5817/AM2012-1-61},
keywords = {Natural operator; linear connection; torsion; reduction theorem; graph},
language = {eng},
issn = {0044-8753},
journal = {Archivum Mathematicum},
title = {Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case},
url = {http://emis.muni.cz/journals/AM/12-1/am2052.pdf},
volume = {48},
year = {2012}
}
Original language:English
Field:General mathematics
WWW:link to a new windowhttp://emis.muni.cz/journals/AM/12-1/am2052.pdf
Type:Article in Periodical
Keywords:Natural operator; linear connection; torsion; reduction theorem; graph
Attached files:link to a new windowAM 2012 42 JanMar.pdf

This paper is a continuation of the paper J. Janyška and M. Markl, Combinatorial differential geometry and ideal Bianchi-Ricci identities, Advances in Geometry 11 (2011) 509-540, dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an `ideal' basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi--Ricci identities without corrections.

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