In " Geometric structures on lowdimensional manifolds " , section 2 , we have : given a projective tame 3manifold with radial ends , each end surface has a projective structure since a developing image from manifold induces a developing map from a component of a neighborhood of an aend which homeomorphic to a surface times R to R3 where lines all map to radial lines from a point.since the set of lines ending at a given point of RP3 form a sphere with projective structure , it follows that each end surface has an induced projective structure ". why the set of lines ending at a given point of RP3 form a sphere with projective structure ?
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