On a New Class of Lifts in the Coframe Bundle

Connections On The Coframe Bundle

“…The complete lift of the symmetric linear connection in the cotangent bundle is defined as the Riemannian connection of the Riemannian extension of the Riemannian metric in the cotangent bundle of a Riemannian manifold (see, [6], [18, p.268]). On the other hand, in article [13], considering the coframe bundle F * M of a Riemannian manifold M , a so-called g-lift of the Riemannian metric g in the coframe bundle F * M is found that is analogous to the Riemannian extension in the cotangent bundle C T (M ):…”

“…Various questions of the differential geometry of the cotangent bundle have been studied by many authors (see, for example, [2], [3], [6], [7], [11], [12], [14], [16], [17]). On the other hand, the some problems concerning differential geometry of F * M has been investigated in [4] by authors of the present paper (see also, [13]). One of the basic differential-geometric structures on a smooth manifold is a linear connection.…”