Related papers: Einstein metrics on some exotic negatively curved …

This paper has been withdrawn by the author due to extremely unscientific errors.

In the following work we investigate the structure of Einstein manifolds with positive scalar curvature whose curvature operator is sufficiently close to the identity operator in dimensions below 12. An Einstein manifold with positive…

Paper withdrawn because of unjustified approximation between equations 13 and 14.

Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context…

This paper has been withdrawn by the authors due to a crucial error.

Starting with a compact hyperbolic cone-manifold of dimension greater than or equal to 3, we study the deformations of the metric with the aim of getting Einstein cone-manifolds. If the singular locus is a closed codimension 2 submanifold…

In this paper we construct a family of examples of self-dual Einstain metrics of neutral signature, which are not Ricci flat, nor locally homogenous. Curvature of these manifolds is studied in details. These are obtained by the…

This paper has been withdrawn by the author, due to an error in Proposition 2.2.

This paper considers the existence of conformally compact Einstein metrics on 4-manifolds. A reasonably complete understanding is obtained for the existence of such metrics with prescribed conformal infinity, when the conformal infinity is…

This paper is devoted to the first systematic investigation of manifolds that are Einstein for a connection with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any…

We prove the existence of three non-round, non-isometric Einstein metrics with positive scalar curvature on the sphere $S^{10}.$ Previously, the only even-dimensional spheres known to admit non-round Einstein metrics were $S^6$ and $S^8.$

This article describes some geometric invariants and conformal anomalies for conformally compact Einstein manifolds and their minimal submanifolds which have recently been discovered via the Anti-de Sitter/Conformal Field Theory…

We develop a notion of Einstein manifolds with skew torsion on compact, orientable Riemannian manifolds of dimension four. We prove an analogue of the Hitchin-Thorpe inequality and study the case of equality. We use the link with…

This paper has been withdrawn by author due to an error in the proof.

We give an elementary treatment of the existence of complete Kahler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n+1)-sphere.

We construct new complete Einstein metrics on smoothly bounded strictly pseudoconvex domains in Stein manifolds. This is done by deforming the K\"ahler-Einstein metric of Cheng and Yau, the approach that generalizes the works of Roth and…

This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.

We find a new obstruction for a real Einstein 4-orbifold with an A1-singularity to be a limit of smooth Einstein 4-manifolds. The obstruction is a curvature condition at the singular point. For asymptotically hyperbolic metrics, with…

Fine and Premoselli (FP) constructed the first examples of manifolds that do not admit a locally symmetric metric but do admit a negatively curved Einstein metric. The manifolds here are hyperbolic branched covers like those used by Gromov…

Paper withdrawn due to error.