Orthochronous Lorentz group
= Orthochronous Lorentz group
{c}
{title2=$O^+(1,3)$}
The orthochronous Lorentz group consists of Lorentz transformations preserving the future sheet of the unit timelike hyperboloid. Equivalently, $A_{00}>0$. This is an open subgroup of $O(1,3)$ and hence a full-dimensional submanifold.