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In " Geometric structures on low-dimensional manifolds " , section 2 , we have : given a projective tame 3-manifold 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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Could you please give us some motivation for this (as per mathoverflow.net/howtoask) –  David Roberts Feb 1 '13 at 5:44
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@DAVID (not David Roberts!): You should first try to understand topology of the space of lines through the given point in the 3-space. Then see if you can figure out by yourself if this space has a natural real projective structure. If you cannot do this, I suggest you start reading a different book (maybe Hatcher's "Algebraic Topology"). –  Misha Feb 1 '13 at 6:22
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