On Affine Connections Induced on the (1, 1)-Tensor Bundle

Let M be an n-dimensional differentiable manifold with an affine connection without torsion and T1 1 (M) its (1, 1)-tensor bundle. In this paper, the authors define a new affine connection on T1 1 (M) called the intermediate lift connection, which lies somewhere between the complete lift connection and horizontal lift connection. Properties of this intermediate lift connection are studied. Finally, they consider an affine connection induced from this intermediate lift connection on a cross-section σξ(M) of T1 1 (M) defined by a (1, 1)-tensor field ξ and present some of its properties. © 2018, Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature.