Left-invariant metrics on a tensor bundle of type (2,0) over a Lie group

Abstract

In this paper, vertical and horizontal lifts of left-invariant vector fields are constructed. Necessary and sufficient conditions for the horizontal lift of left-invariant vector fields to be left-invariant field are established. On the basis of a left-invariant metric on G, left-invariant vertical and horizontal distributions and a left-invariant metric g on T0 2G are constructed. © 2013 Pleiades Publishing, Ltd.