Picture below is from Li and Yau's Estimates of eigenvalues of a compact Riemannian manifold. How to get the (1.8) ? The main difficult is how to get the term with curvature. I guess it is because $u_{jii}$ become $u_{iij}$, but $u$ just a function, exchange the partial derivative will not creat term with curvature.
Besides, I found I am puny to calculate exchange partial derivative, whether there are some suitable example or exercise.
