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{title2=$\nabla_bk_a=0$}

A one-form $k$ with $\nabla_bk_a=0$. If $\ell=d\phi$ satisfies $\nabla_b\ell_a+\ell_a\ell_b=0$, then $k=e^\phi\ell=d(e^\phi)$ is parallel.


Parallel covector field

Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 3 / 35D / d / Solution

Parallel covector field ( $\nabla_{b} k_{a} = 0$ )

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Parallel covector field (∇b​ka​=0)

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Parallel covector field ( $\nabla_{b} k_{a} = 0$ )

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