UC Riverside

Higgs Bundles are known as a useful tool to study the topology of moduli spaces. Only recently was it known that they could provide information about specific representations. This thesis will focus on a class of SU(n + 1, 1)-Higgs bundles which can provide specific information about their associated representations, as well as construct a family of complex hyperbolic structures on associated manifolds.We prove that these Higgs bundles correspond to Anosov representations and in the case of SU(2, 1), they parametrize a family of convex cocompact representations that achieve every Toledo invariant and thus lie in every component of the character variety MB(X, SU(2, 1)), recovering a historical result with new methods. In addition, we prove analogous results for a class of SO0(2, n + 2)-Higgs bundles, namely, that they correspond to Anosov representations and can be used to parametrize a class of geometric structures on specific manifolds.