Two-sheeted hyperboloid
= Two-sheeted hyperboloid
{title2=$t^2-x^2-y^2=1$}
This <regular surface> has two connected components, $t=\pm\sqrt{1+x^2+y^2}$. The <symmetric-matrix model of the two-sheeted hyperboloid> realizes them as the positive-definite and negative-definite symmetric determinant-one $2\times2$ matrices. Each component is diffeomorphic to $\mathbb R^2$; this differs from the connected <one-sheet hyperboloid>.