Derivatives with Respect to Lifts of the Riemannian Metric of the Format fG˜ =S gf +H g on TM Over a Riemannian Manifold (M, g).

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In this paper, we define the Riemannian metric of the format fG˜ =S gf +H g on TM over (M, g) Riemannian manifold , which is completely determined by vector fields β H and θ V . Later, we obtain the covarient and Lie derivatives applied to the Riemannian metric of the format fG˜ =S gf +H g with respect to the vertical XV and horizontal lifts XH of vector fields, respectively.

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Has¸im C¸ AYIR. (2019) Derivatives with Respect to Lifts of the Riemannian Metric of the Format fG˜ =S gf +H g on TM Over a Riemannian Manifold (M, g)., , Volume 51, Issue 1.

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Derivatives with Respect to Lifts of the Riemannian Metric of the Format fG˜ =S gf +H g on TM Over a Riemannian Manifold (M, g).

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