Lifts of connections to the bundle of (1,1) type tensor frames
11Department of Algebra and Geometry, Faculty of Mechanics and Mathematics, Baku State University, Baku, Azerbaijan
2Department of Mathematics, Faculty of Arts and Sciences, Giresun University, Giresun, Turkey
2Department of Mathematics, Faculty of Arts and Sciences, Giresun University, Giresun, Turkey
Sigma J Eng Nat Sci 2021; 39(2): 177-183 DOI: 10.14744/sigma.2021.00007
Abstract
In this paper we consider the bundle of (1,1) type tensor frames over a smooth manifold, define the horizontal and complete lifts of symmetric linear connection into this bundle. Also we study the properties of the geodesic lines corresponding to the complete lift of the linear connection and investigate the relations between Sasaki metric and lifted connections on the bundle of (1,1) type tensor frames.
Keywords: Bundle of (1,1) type tensor frame, linear connection, adapted frame, horizontal lift, complete lift, geodesic line, Sasaki metric, metrical connection
