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In $H$ you have two lightlike geodesics such that every lightlike geodesic intersects one of these two, namely the geodesics $\{x=y\}$ and $\{x=-y\}$. In $S$ you do not have such two geodesics. Hence, the regions are not conformally equivalent
In $H$ you have two lightlike geodesics such that every geodesic intersects one of these two, namely the geodesics $\{x=y\}$ and $\{x=-y\}$. In $S$ you do not have such two geodesics. Hence, the regions are not conformally equivalent
In $H$ you have two lightlike geodesics such that every lightlike geodesic intersects one of these two, namely the geodesics $\{x=y\}$ and $\{x=-y\}$. In $S$ you do not have such two geodesics. Hence, the regions are not conformally equivalent
In $H$ you have two lightlike geodesics such that every geodesic intersects one of these two, namely the geodesics $\{x=y\}$ and $\{x=-y\}$. In $S$ you do not have such two geodesics. Hence, the regions are not conformally equivalent
