Linear Connections with and without Torsion, Making Parallel an Integrable Endomorphism on a Manifold

Abstract

Our study is developed in a general framework, namely a manifold M endowed with a (1,1)-tensor field φ, 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 φ.
To count all these connections with the given properties, certain algebraic techniques and results are used throughout the paper.