A connection on a principal bundle $\pi:P\rightarrow M$ is a choice of horizontal subspace $H_p$ at each $p\in P$, such that $T_p P = H_p + V_p$ where $V_p = \ker((\pi_*)_p)$. It is very common to write an arbitrary element of $T_p P$ as the sum of its vertical and horizontal components. My question relates to a paper I am currently reading - a screenshot of a page is found below:
I was wondering if anyone knows what the $\mathbf{R}$ notation the author uses in the decomposition of $T_{u(t)}P$ is? I have gone through the rest of the paper and can't seem to find the definition anywhere. If anyone has an idea of what this is, then it would be much appreciated if you could let me know!