DERIVATIVES WITH RESPECT TO COMPLETE AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC ON COTANGENT BUNDLE

Abstract

In this paper, we define the Cheeger-Gromoll metric in the cotangent bundle , which is completely determined by its actionon complete lifts of vector fields. Later, we obtain the covariant and Lie derivatives applied to Cheeger-Gromoll metrics with respect to the complete and vertical lifts of vector and kovector fields, respectively.