# What does the notation $\nabla_g f$ mean?

I am trying to parse this expression:

$(\nabla_{\nabla p \times e_1} \nabla p) \times \nabla p$

The setup is that $p$ is a polynomial in $\mathbb{R}[x,y,z]$ and $e_1 = (1,0,0)$ is one of the standard basis vectors for $\mathbb{R}^3$. The part I haven't encountered before is the notation $\nabla_g f$ so I would like to know what that means. Thank you!

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 This helps: en.wikipedia.org/wiki/Covariant_derivative – user32240 Aug 8 '12 at 22:57