However, only in some specific directions V 0 : ( s 0 , w 0 ) , will the bent light rays reach the observer, i.e., the images only form where D = δ δ V = 0 | ( s 0 , w 0 ) . Then we can directly apply the Poincaré–Hopf theorem χ χ = ∑ ∑ index D = constant .