Let $(M, \langle.,.\rangle )$ be a 2-dimensional Riemannian manifold, $\nabla$ its Levi-Civita connection. How can I show that there is a function $K \in \mathscr C^{\infty}(M)$ such that $$R^{\nabla}(X,Y)Z=K(\langle Y,Z\rangle X-\langle X,Z \rangle Y) $$ for all $X,Y,Z \in \Gamma (TM)$?
Would appreciate some help or approach to solve this, thanks in advance.