Abstract:
In this research we study the curvature of almost Hermition manifolds and their special analogues via intrnsic torsion and representation theory. We also investigate that the compact 7-dimensional manifold equipped with G_2-Structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G_2. Also we illustrate that Bryant’s weak holonomy metric on the homology seven-sphere is the unique weak metric arising from a rational curve.
