Horizontal lift of linear connections to vector bundles associated with the principal bundle of linear frames

In this study, horizontal lift of linear connections to vector bundles associated with the principal bundle of linear frames of any differentiate manifold M was investigeted. The two important results of teorem 3.3.1. were given. Beside, in the theorem 3.3.3 and 3.3.5 torsion tensor and curvature tensor of V linear connection on E total space are given respectively. Theorem 3.3.6 and 3.3.7. generalize similar theorem proved by K.Yano and S.lshihara in the case of tangent bundles and by K.Yano and E.M. Patterson in the case of cotangent bundles. Key Words Associated fibre bundle, principal bundle, horizontal lift