In this paper, we define the Cheeger-Gromoll metric in the $(1,1)$ $-$tensor bundle $T_{1}^{1}(M)$, 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.
(1 1)-tensor bundle Covarient Derivative Lie Derivative Cheeger-Gromoll metric Horizontal Lift Vertical Lift
Subjects | Engineering |
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Journal Section | Articles |
Authors | |
Publication Date | October 15, 2017 |
Submission Date | October 13, 2017 |
Acceptance Date | May 31, 2017 |
Published in Issue | Year 2017 Volume: 5 Issue: 2 |