NON-KAHLER EXPANDING RICCI SOLITONS, EINSTEIN METRICS, AND EXOTIC CONE STRUCTURES

We consider complete multiple warped product type Riemannian metrics on manifolds of the form R-2 x M-2 x ... x M-r, where r >= 2 and M-i are arbitrary closed Einstein spaces with positive scalar curvature. We construct on these spaces a family of non-Kahler, non-Einstein, expanding gradient Ricci solitons with conical asymptotics as well as a family of Einstein metrics with negative scalar curvature. The 2-dimensional Euclidean space factor allows us to obtain homeomorphic but not diffeomorphic examples which have analogous cone structure behaviour at infinity. We also produce numerical evidence for complete expanding solitons on the vector bundles whose sphere bundles are the twistor or Sp(1) bundles over quaternionic projective space.