Editing Covariant derivative (section)

===Covector fields===
Given a field of [[Cotangent space|covectors]] (or [[one-form]]) <math>\alpha</math> defined in a neighborhood of {{mvar|p}}, its covariant derivative <math>(\nabla_\mathbf{v}\alpha)_p</math> is defined in a way to make the resulting operation compatible with tensor contraction and the product rule. That is, <math>(\nabla_\mathbf{v}\alpha)_p</math> is defined as the unique one-form at {{mvar|p}} such that the following identity is satisfied for all vector fields {{math|'''u'''}} in a neighborhood of {{mvar|p}}
<math display="block">\left(\nabla_\mathbf{v}\alpha\right)_p \left(\mathbf{u}_p\right) = \nabla_\mathbf{v}\left[\alpha\left(\mathbf{u}\right)\right]_p - \alpha_p\left[\left(\nabla_\mathbf{v}\mathbf{u}\right)_p\right].</math>

The covariant derivative of a covector field along a vector field {{math|'''v'''}} is again a covector field.