Definite quadratic form

runs over the reduced（英语：Binary quadratic form#Reduction and class numbers） binary quadratic forms（英语：Binary quadratic form） a x 2 + b x y + c y 2 {\textstyle

two sheets. The induced metric in this case is positive-definite（英语：Definite quadratic form）, and each sheet is a copy of hyperbolic n-space（英语：hyperbolic

) {\displaystyle (qu)(tu)^{*}=(uu^{*})q(t^{*})} 。 The quadratic form qq∗ is positive definite on the planes Cv and N. Consider the counter-sphere {q: