I'm reading John M. Lee's book " Riemannian Manifolds". On page 57, the covariant derivative of $V$ along a curve $\gamma$ is defined, where $V$ is a vector field along $\gamma$. It is denoted by $D\_tV$.

So why is the subscript is $t$? Why not $\gamma$?

When $D\_tV$ is evaluated at $t\_0$, it is written as $D\_tV(t\_0)$. So it is not a variable, right? I'd like to know what the subscript $t$ stands for.