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5.1 It is shown in the text that the covariant derivative of a vector is given by $v^i_{;j} = \frac{\partial v^i}{\partial q^j} + \Gamma^i_{jk} v^k$ $v_{i;j} = \frac{\partial v_i}{\partial q^j} - \Gamma^k_{ij} v_k$ It is also shown that the metric is constant under covariant differentiation so that it can be moved through the derivative to raise and lower indices. Thus $g_{ik} (v^k_{;j}) = v_{i;j}$ Use this relation to derive the second of the above equations from the first.

          5.1 It is shown in the text that the covariant derivative of a vector is
given by
$v^i_{;j} = \frac{\partial v^i}{\partial q^j} + \Gamma^i_{jk} v^k$
$v_{i;j} = \frac{\partial v_i}{\partial q^j} - \Gamma^k_{ij} v_k$
It is also shown that the metric is constant under covariant differentiation
so that it can be moved through the derivative to raise and lower indices.
Thus
$g_{ik} (v^k_{;j}) = v_{i;j}$
Use this relation to derive the second of the above equations from the first.

5.1 It is shown in the text that the covariant derivative of a vector is
given by
v^i;j = (∂ v^i)/(∂ q^j) + Γ^ijk v^k
vi;j = (∂ vi)/(∂ q^j) - Γ^kij vk
It is also shown that the metric is constant under covariant differentiation
so that it can be moved through the derivative to raise and lower indices.
Thus
gik (v^k;j) = vi;j
Use this relation to derive the second of the above equations from the first.

Added by Kimberly E.

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