DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$

Authors : HAŞİM ÇAYIR, MOHAMMAD NAZRUL ISLAM KHAN

Pages : 78-86

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Publication Date : 2017-10-15

Article Type : Research Paper

Abstract :In this paper, we define the Cheeger-Gromoll metric in the $insert ignore into journalissuearticles values(1,1);$ $-$tensor bundle $T_{1}^{1}insert ignore into journalissuearticles values(M);$, which is completely determined by its action on vector fields of type $X^{H}$ and $\omega ^{V}$. Later, we obtain the covarient and Lie derivatives applied to the Cheeger-Gromoll metric with respect to the horizontal and vertical lifts of vector and kovector fields, respectively.
Keywords : 1 1, tensor bundle, Covarient Derivative, Lie Derivative, Cheeger Gromoll metric, Horizontal Lift, Vertical Lift