F. Michael, R. Atiyah, and . Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A, vol.308, issue.1505, pp.523-615, 1983.

D. Baraglia, Cyclic Higgs bundles and the affine Toda equations, arXiv.org, 2010.

Y. Benoist and D. Hulin, Cubic differentials and hyperbolic convex sets, Journal of Differential Geometry, vol.98, issue.1, pp.1-23, 2013.

B. Berndtsson, Curvature of vector bundles associated to holomorphic fibrations, Annals of Mathematics, vol.169, issue.2, pp.531-560, 2009.

J. Bolton, F. Pedit, and L. Woodward, Minimal surfaces and the affine Toda field model, Journal für die Reine und Angewandte Mathematik, vol.459, pp.119-150, 1995.

F. Bonsante and J. Schlenker, Maximal surfaces and the universal Teichm??ller space, Inventiones mathematicae, vol.28, issue.2, pp.279-333, 2010.

N. Bourbaki, Lie groups and Lie algebras, Elements of Mathematics, vol.79, 2005.

B. Steven, O. Bradlow, . García-prada, B. Peter, and . Gothen, Deformations of maximal representations in Sp, The Quarterly Journal of Mathematics, vol.4, issue.63 4, pp.795-843, 2012.

M. Bridgeman, R. Canary, F. Labourie, and A. Sambarino, The pressure metric for convex representations, arXiv.org, 2013.

B. Collier and Q. Li, Asymptotics of certain families of Higgs bundles in the Hitchin component, arXiv.org, 2014.

J. Demailly, Analytic methods in algebraic geometry, Surveys of Modern Mathematics, vol.1

K. Simon and . Donaldson, Twisted harmonic maps and the self-duality equations, Proceedings of the London Mathematical Society. Third Series, vol.55, issue.1, pp.127-131, 1987.

V. Vladimir, A. B. Fock, and . Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci, issue.103, pp.1-211, 2006.

O. García-prada, B. Peter, I. Gothen, and . Mundet-i-riera, Higgs bundles and surface group representations in the real symplectic group, Journal of Topology, vol.6, issue.1, pp.64-118, 2013.

O. García-prada and I. Mundet-i-riera, Representations of the fundamental group of a closed oriented surface in Sp, Topology, vol.4, issue.43 4, pp.831-855, 2004.

M. William and . Goldman, The symplectic nature of fundamental groups of surfaces Convex real projective structures on closed surfaces are closed, Proc. Amer, pp.200-225, 1984.

A. Phillip and . Griffiths, Hermitian differential geometry and the theory of positive and ample holomorphic vector bundles, J. Math. Mech, vol.14, pp.117-140, 1965.

O. Guichard and A. Wienhard, Convex foliated projective structures and the Hitchin component for ${\rm PSL}_4(\mathbf{R})$, Duke Mathematical Journal, vol.144, issue.3, pp.381-445, 2008.

J. Nigel and . Hitchin, The self-duality equations on a Riemann surface, Proceedings of the London Mathematical Society Lie groups and Teichmüller space, pp.59-126, 1987.

A. Katok, Entropy and closed geodesics, Ergodic Theory Dynam, Systems, vol.2, issue.3-4, pp.339-365, 1982.

I. Kim and G. Zhang, Kahler metric on Hitchin component, arXiv.org, 2013.

S. Kobayashi, Differential geometry of complex vector bundles, 1987.

B. Kostant, The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group, Lie group representations on polynomial rings, pp.973-1032, 1959.
DOI : 10.2307/2372999

Q. Li, Teichmüller Space Is Totally Geodesic In Goldman Space, arXiv.org, 2013.

C. John and . Loftin, Affine spheres and convex RP n -manifolds, American Journal of Mathematics, vol.123, issue.2, pp.255-274, 2001.

J. Sacks and K. Uhlenbeck, The Existence of Minimal Immersions of 2-Spheres, Minimal immersions of closed Riemann surfaces, pp.1-24, 1981.
DOI : 10.2307/1971131

M. Richard and . Schoen, The role of harmonic mappings in rigidity and deformation problems, Complex geometry, pp.179-200, 1990.

M. Richard, S. Schoen, and . Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Annals of Mathematics, vol.110, issue.1, pp.127-142, 1979.

T. Carlos and . Simpson, Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, J. Amer. Math. Soc, vol.1, issue.4, pp.867-918, 1988.

M. Wolf, The Teichm??ller theory of harmonic maps, Journal of Differential Geometry, vol.29, issue.2, pp.449-479, 1989.

A. Scott and . Wolpert, Chern forms and the Riemann tensor for the moduli space of curves, Inventiones Mathematicae, vol.85, issue.1, pp.119-145, 1986.