The standard contact structure on $\mathbb R^{2n+1}=(x\_1,y\_1,\dots,x\_n,y\_n,z)$ is given by $\ker\alpha$, where $\alpha=dz-\sum\_{i=1}^ny\_idx\_i$. But is there a reason why this contact structure is called "standard"? Is it just convention, or because it's the "nicest" contact structure, or is this contact structure actually natural in some important way?



Why is the standard contact structure on $\mathbb R^{2n+1}$ called "standard"?
I agree that Darboux' theorem is a very good reason for calling this "standard".


Another reason is that it (one-point-)compactifies to the standard contact structure on the $(2n+1)$-sphere: this is the space of complex tangencies to $S^{2n+1}$, viewed as the unit sphere in $\mathbb{C}^{n+1}$.


