Open AccessLinear connections with and without torsion, making parallel an integrable endomorphism on a manifold
Author(s) -
Cornelia-Livia Bejan,
M Ana Velimirovic
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1910943b
Subject(s) - mathematics , endomorphism , torsion (gastropod) , integrable system , algebraic number , pure mathematics , manifold (fluid mechanics) , algebra over a field , vector field , mathematical analysis , geometry , engineering , medicine , mechanical engineering , surgery
Our study is developed in a general framework, namely a manifold M endowed with a (1,1)- tensor field ?, which is integrable. The present paper solves the following two problems: how many linear connections with torsion and without torsion exist, having the property of being parallel with respect to ?. To count all these connections with the given properties, certain algebraic techniques and results are used throughout the paper.