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 T ₁ ¹ (M) its (1, 1)-tensor bundle. In this paper, the authors define a new affine connection on T ₁ 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 σ_ξ(M) of T ₁ ¹ (M) defined by a (1, 1)-tensor field ξ and present some of its properties.