I am self-studying the theory of minimal surfaces from Colding-Minicozzi's "A Course in Minimal Surfaces". In section $8$ of the first Chapter (to be more precise page 40) they derive the second variation formula for the volume functional. I have a question regarding that. The situation is as follows :
$\Sigma^k\subset M^n$ is a minimal submanifold and $F$ is a variation of $\Sigma$ with compact support. $F$ is assumed to be a normal variation, i.e., $F_{t}^T=0$. Now they derive the second variation and they get the formula
$$\frac{d^2}{dt^2}\bigg|_{t=0}(\text{Vol}(F(\Sigma,t)))=-\int_{\Sigma}\langle F_t, LF_t\rangle$$
where $L$ is the $stability \ operator$ defined as follows
$$LX=\Delta^{N}_\Sigma X+\tilde{A}(X)+\text{Tr}[Rm_M(\cdot,X)\cdot].$$
where $X$ is normal vector field to $\Sigma$, Rm$_M$ is the Riemann Curvature tensor of $M$ and $\tilde{A}$ is the Simons' operator.
Now they say that $L$ is a self-adjoint and hence $LX$ should be a normal vector field to $\Sigma$. Clearly the first term in the definition of $L$ is normal to $\Sigma$, $\tilde{A}$ by definition is normal to $\Sigma$ as well.
My question is that why is the term $\text{Tr}[Rm_M(\cdot,X)\cdot]$ normal to $\Sigma$ ?