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MR1180262 (93i:53062) 53C45 (52A55 53A30)
Labourie, François Surfaces convexes dans l'espace hyperbolique et $C{\rm P}\sp 1$-structures. (French) [Convex surfaces in hyperbolic space and $C{\rm P}\sp 1$-structures] J. London Math. Soc. (2) 45 (1992), no. 3, 549--565.
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