Einstein metrics on bundles over quaternionic-Kähler manifolds

In this thesis, we investigate the Einstein metrics on a rank-three bundle defined over a 4n-dimensional quaternionic Kähler base manifold. Defining Riemannian metrics and pseudo-Riemannian metrics of signature (4n,3) on the bundle, we find the connection forms and calculate their curvatures. Then, we obtain the Ricci curvatures by contracting the curvatures. Finally, we examine the case of Ricci curvature zero and compare our results with the results in the literature.