Zubrilin K. Flattening properties of the diffeomorphisms of the tangent bundles, induced by geodesic, concircular and holomorphically projective diffeomorphisms of the bases

The thesis is devoted to investigation of the flattening properties of the induced diffeomorphisms. In particular, results concerning the use of the capture of an affine connection for the study of the flattening properties of the diffeomorphisms are obtained. Tensors of an affine deformation of the induced diffeomorphisms are constructed. The concept of an E-lift of a tensor field of type (1,1) is introduced and its properties, which enable to calculate the covariant derivative relative to the connection of a horizontal lift are investigated. As concerning the tangent bundle with a connection of a horizontal lift, the flattening properties of the diffeomorphism induced by the geodesic diffeomorphism are investigated. In relation to the tangent bundle of a second order with a connection of the II-lift, flattening properties of the transformation induced by a concircular transformation of a (pseudo) Riemannian space are investigated. The flattening properties of holomorphically projective diffeomorphism of the Kahler manifold are investigated. As concerning the tangent bundle with the connection of a complete lift, flattening properties of the diffeomorphism induced by the holomorphically projective diffeomorphism are studied