First picture below is from Topping's Lectures on the Ricci flow. I don't understand the red line.
I read the holonomy in Wiki, I understand the second picture which is from Wiki. But I fail to know the strict definition of holonomy.
I want to know why $R(X,Y)$ is the infinitesimal holonomy rotation from second picture ? And why it leads a natural definition of curvature operator ?
PS: $Rm(X,Y,W,Z)= \langle R(X,Y)W,Z\rangle$
