I'm a student, trying to re-derive a result found in a paper by calculating the following in spherical coordinates:
$$\mathbf{I}+ \frac{\nabla\nabla}{\mathrm{constant}},$$
where $\mathbf{I}$ is a $3\times 3$ identity matrix.
The paper that I've seen writes the result as
\begin{bmatrix} 0 & 0 & 0\\ \cos(\Theta)\cos(\Phi) & \cos(\Theta)\sin(\Phi) & -\sin(\Theta)\\ -\sin(\Phi) & \cos(\Theta) & 0 \end{bmatrix}
How do they get that? What is the gradient of a gradient in spherical coordinates? Is it a Hessian?
Please see equations 11 and 13 of the following paper: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.369.921&rep=rep1&type=pdf
It's the Vector Laplacian, which is kind of like a Hessian. You can find a spherical coordinate version of it here.