In this paper, the equality
$$ |Du| \text{div}\left( \frac{Du}{|Du|}\right) = \left( \delta_{ij} - \frac{u_{x_i}u_{x_j}}{|Du|^2} \right) u_{x_ix_j} $$
is asserted without explanation for $u: \mathbb{R}^n \to \mathbb{R}$. Further, the notation, $\delta_{ij}$, is left undefined. The LHS is a scalar, while the RHS seems to imply components of $n \times n$ matrix (unless summation is implied?).
Is the notation on the RHS standard? Once the notation is established on the RHS, does equality to the LHS easily follow? If not, is there a reference for the equality?
Hint: use $$ Du=(u_{x_1}, \cdots, u_{x_n}), |Du|=\sqrt{u_{x_1}^2 \cdots+u_{x_n}^2},\text{Div}(v_1,\cdots,v_n)=\sum_{i=1}^n\frac{\partial v_i}{\partial x_i}$$