Covariant derivative

• How Is the Second Covariant Derivative of a Scalar Computed?
  Compute a scalar's second covariant derivative by differentiating its gradient as a covector and subtracting the Christoffel-symbol term.
• What Is the Coordinate-Free Definition of the Nabla Operator?
  Nabla is not one universal coordinate-free vector: the gradient comes from a metric, while covariant differentiation comes from a connection.