Results: **3**

#### Giving the 1st order affine connection by means of the 2nd order vector-valued forms

Affine connection is given by 2nd order vectors called horizontal. Vertical and horizontal forms of 2nd order are entered for 1st order affine connection. It is proved that symmetric affine connection in the **bundle** of **tangent** linear frames defines vertical linear operator (a vertical vertical-valued form of 2nd order for 1st order affine connection) from 2nd order **tangent** space into 1st order **tangent** space to a manifold. It is shown that affine connection in **bundle** ...

#### About horizontally vector lifts of tensor fields from the base to its **tangent** **bundle**

The vector field of the type , obtained fr om the tensor field on a smooth manifold M to the **tangent** **bundle** , arises in the study of infinitesimal affine transformations with a complete lift. The H-lift was introduced S. Tanno in 1974 in infinitesimal isometries on the **tangent** **bundle** with the complete lift. The definition of H’-lift given by ...

#### Connection in a **tangent** **bundle** to the frame **bundle** of manifold

This paper focuses on the **tangent** **bundle** to the linear frame **bundle** of a smooth manifold. Brackets of the **tangent** vectors of this **bundle** are con-structed. A coordinate representation of the non-holonomic frame vectors is produced. Horizontal and vertical curvatures, torsions, and covariant ...