We obtain new examples of non-symmetric Einstein solvmanifolds by combining two techniques. In Tamaru (Parabolic subgroups of semisimple Lie groups and einstein solvmanifolds. Math Ann 351(1):51–66, 2011) constructs new attached solvmanifolds, which are submanifolds of the solvmanifolds correspond to noncompact symmetric spaces, endowed with a natural metric. Extending this construction, we app...

We consider S 2 bundles P and P ′ of totally null planes of maximal dimension over a 4-dimensional manifold equipped with a Weyl or Riemannian geometry. The fibre product PP ′ of P and P ′ is found to be appropriate for the encoding of both the selfdual and the Einstein-Weyl equations for the 4-metric. This encoding is realized in terms of the properties of certain well defined geometrical obje...

We show that there exist smooth, simply connected, fourdimensional spin manifolds which do not admit Einstein metrics, but nonetheless satisfy the strict Hitchin-Thorpe inequality. Our construction makes use of the Bauer/Furuta cohomotopy refinement of the Seiberg-Witten invariant [3, 9], in conjunction with curvature estimates previously proved by the second author [17]. These methods also all...

A Hermitian Einstein-Weyl manifold is a complex manifold admitting a Ricci-flat Kähler covering M̃ , with the deck transform acting on M̃ by homotheties. If compact, it admits a canonical Vaisman metric, due to Gauduchon. We show that a Hermitian Einstein-Weyl structure on a compact complex manifold is determined by its volume form. This result is a conformal analogue of Calabi’s theorem stating ...

We construct two classes of higher-derivative supergravity theories generalizing Einstein supergravity. We explore their dynamical content as well as their vacuum structure. The first class is found to be equivalent to Einstein supergravity coupled to a single chiral superfield. It has a unique stable vacuum solution except in a special case, when it becomes identical to a simple no-scale theor...

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar ...