Compact four-dimensional Einstein manifolds

Compact Einstein-Weyl four-dimensional manifolds

We look for complete four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. Using the explicit 4-parameters expression of the distance obtained in a previous work for non-conformally-Einstein Einstein-Weyl structures, we show that four 1-parameter families of compact metrics exist : they are all of Bianchi IX type and conformally Kähler ; moreover, in agreement with general resul...

Four - Manifolds without Einstein

Einstein structures on four-dimensional nutral Lie groups

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

Four-manifolds without Einstein Metrics

It is shown that there are infinitely many compact simply connected smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2χ > 3|τ |. The examples in question arise as non-minimal complex algebraic surfaces of general type, and the method of proof stems from Seiberg-Witten theory.

Nonlinear Schrödinger Equation on Four - Dimensional Compact Manifolds

— We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadr...