Boletim da Sociedade Paranaense de Matematica, vol.41, 2023 (ESCI)
© 2023 Boletim da Sociedade Paranaense de Matematica. All rights reserved.In the present paper, a Riemannian metric on the tangent bundle, which is another generalization of Cheeger-Gromoll metric and Sasaki metric, is considered. This metric is known as Kaluza-Klein metric in literature which is completely determined by its action on vector fields of type XH and Y V . We obtain the covarient and Lie derivatives applied to the Kaluza-Klein metric with respect to the horizontal and vertical lifts of vector fields, respectively on tangent bundle TM.