Let $S$ be a $2n$-dimensional complex manifold equipped with a line bundle with a real-analytic complex connection such that its curvature is of type $(1,1)$, and with a real analytic h-projective structure such that its h-projective curvature is of type $(1,1)$. For $n=1$ we assume that $S$ is equipped with a real-analytic M\"obius structure. Using the structure on $S$, we construct a twistor space of a quaternionic $4n$-manifold $M$. We show that $M$ can be identified locally with a neighbourhood of the zero section of the twisted (by a unitary line bundle) tangent bundle of $S$ and that $M$ admits a quaternionic $S^1$ action given by unit scalar multiplication in the fibres. We show that $S$ is a totally complex submanifold of $M$ and that a choice of a connection $D$ in the h-projective class on $S$ gives extensions of a complex structure from $S$ to $M$. For any such extension, using $D$, we construct a hyperplane distribution on $Z$ which corresponds to the unique quaternionic connection on $M$ preserving the extended complex structure. We show that, in a special case, the construction gives the Feix--Kaledin construction of hypercomplex manifolds, which includes the construction of hyperk\"ahler metrics on cotangent bundles. We also give an example in which the construction gives the quaternion-K\"ahler manifold $\mathbb{HP}^n$ which is not hyperk\"ahler. We show that the same construction and results can be obtained for $n=1$. By convention, in this case, $M$ is a self-dual conformal $4$-manifold and from Jones--Tod correspondence we know that the quotient $B$ of $M$ by an $S^1$ action is an asymptotically hyperbolic Einstein--Weyl manifold. Using a result of LeBrun \cite{Le}, we prove that $B$ is an asymptotically hyperbolic Einstein--Weyl manifold. We also give a natural construction of a minitwistor space $T$ of an asymptotically hyperbolic Einstein--Weyl manifold directly from $S$, such that $T$ is the Jones--Tod quotient of $Z$. As a consequence, we deduce that the Einstein--Weyl manifold constructed using $T$ is equipped with a distinguished Gauduchon gauge.

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Cette thèse est consacrée à l'étude des variétés projectives strictement convexes de volume fini. Une telle variété est le quotient G\U d'un ouvert proprement convexe U de l'espace projectif réel RP^(n-1) par un sous-groupe discret sans torsion G de SLn(R) qui préserve U. Dans un premier temps, on étudie l'adhérence de Zariski des holonomies de variétés projectives strictement convexes de volume fini. Pour une telle variété G\U, on montre que, soit G est Zariski-dense dans SLn(R), soit l'adhérence de Zariski de G est conjuguée à SO(1,n-1). On s'intéresse ensuite à l'espace des modules des structures projectives strictement convexes de volume fini. On montre en particulier que cet espace des modules est un fermé de l'espace des représentations. / In this thesis, we study strictly convex projective manifolds of finite volume. Such a manifold is the quotient G\U of a properly convex open subset U of the real projective space RP^(n-1) by a discrete torsionfree subgroup G of SLn(R) preserving U. We study the Zariski closure of holonomies of convex projective manifolds of finite volume. For such manifolds G\U, we show that either the Zariski closure of G is SLn(R) or it is a conjugate of SO(1,n-1).We also focuss on the moduli space of strictly convex projective structures of finite volume. We show that this moduli space is a closed set of the representation space.