Affine transformations of the tangent bundle with a complete lift connection over a manifold with a linear connection of special type

Abstract

In this paper we obtain exact upper bounds for the dimensions of Lie al­ge­bras of infinitesimal affine transformations in tangent bundles with a comp­lete lift connection in the case when the base space is a manifold equipped with a non-projective Euclidean linear connection of a special type.

Keywords

• differentiable manifold
• tangent bundle
• complete lift of li­near connection
• vertical lift of vector fields
• complete lift of vector fields
• vertical-vector lift of affinor
• horizontally-vector lift of affinor
• in­fi­nitesimal affine transformation
• lie algebra