= Oriented orthonormal frame bundle of Minkowski spacetime
{title2=$\mathbb R^{3,1}\rtimes SO(3,1)\longrightarrow\mathbb R^{3,1}$}
An oriented pseudo-orthonormal frame in <Minkowski spacetime> consists of its base point $a$ and a Lorentz matrix $L$ acting on a fixed reference frame. The pairs $(a,L)$ form the <Poincaré group>, and right multiplication by $(0,h)$ sends the frame to $(a,Lh)$ while fixing its base point. Thus the displayed projection is a <principal bundle> with group $SO(3,1)$. The full frame bundle uses $O(3,1)$; a specified time orientation restricts to the corresponding connected component.
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