Solution
= Solution
Metric compatibility and the ordinary chain rule give
$$
\frac d{d\lambda}(g(U,W))
=T^\alpha\nabla_\alpha(g(U,W))
=g(\nabla_TU,W)+g(U,\nabla_TW),
$$
which in components is the required identity.
= Solution
Metric compatibility and the ordinary chain rule give
$$
\frac d{d\lambda}(g(U,W))
=T^\alpha\nabla_\alpha(g(U,W))
=g(\nabla_TU,W)+g(U,\nabla_TW),
$$
which in components is the required identity.