Let $x_0\in \mathbb{R}^2$ and define the backward heat kernel relative to $(x_0, T )$ as
$\rho_{x_0}(x,t)=\frac{e^{-\frac{|x-x_0|^2}{4(T-t)}}}{\sqrt{4\pi(T-t)}}$.
The article that I'm reading says that
where
$\gamma$ is a curve,
$div^\top \ $ means tangential divergence,
$s$ is the arcleght parameter,
$\tau$ is the unit tangent vector to $\gamma$,
$\nu$ is the unit normal vector to $\gamma$,
$\underline{v}$ in the velovity of the point $\gamma(x,t)$,
$\lambda$ is the tangential velocity of the point $\gamma(x,t)$,
$k$ is curvature at the point $\gamma(x,t)$.
Moreover, we set $\underline{\lambda} = \lambda\tau$ and $\underline{k} = k\nu$, then, it clearly follows that $\underline{v} = \underline{\lambda} + \underline{k}$.
Now, I can't understand how to transition from the first line of the formula to the second.