Symmetric Hessian of a scalar field
= Symmetric Hessian of a scalar field
For a torsion-free connection, $U_\mu=\partial_\mu\phi$ satisfies $\nabla_\alpha U_\beta=\nabla_\beta U_\alpha$.
= Symmetric Hessian of a scalar field
For a torsion-free connection, $U_\mu=\partial_\mu\phi$ satisfies $\nabla_\alpha U_\beta=\nabla_\beta U_\alpha$.