Geometric objects related to the exceptional lie groups G_2 and Spin(7) have become increasingly popular in the recent years. Especially so after Bryant's (and others') work which showed the existence of riemannian manifolds with holonomy group equal to one of these groups [Bry87]. However, not much attention is given to the complex manifestations of these objects. This thesis consists of two parts which fills some of these gaps.In the first part of this thesis, we investigate the Cayley Grassmannian (over C) which is the set of four-planes that are closed under a three-fold cross product in C^8. We define a torus action on the Cayley Grassmannian. Using this action, we prove that the minimal compactification is a singular variety. We also show that the singular locus is smooth and has the same cohomology ring as that of CP^5. Furthermore, we identify the singular locus with a quotient of G_2^C by a parabolic subgroup.In the second part of this thesis, we introduce the notion of (almost) G_2^C-manifolds with compatible symplectic structures. Further, we describe "complexification" procedures for a G_2 manifold M inside M_C. As an application we show that isotropic deformations of an associative submanifold Y of a G_2 manifold inside of its complexification M_C is given by Seiberg-Witten type equations.
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