相关论文: Einstein metrics on some exotic negatively curved …
We show that if a closed manifold of dimension at least four admits a negatively curved metric that is almost Einstein in a suitable sense, then it admits a genuine Einstein metric of negative sectional curvature. Importantly, the pinching…
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
This paper has been withdrawn by the author due to serious error found in main argument.
In this paper, we obtain classification of four-dimensional Einstein manifolds with positive Ricci curvature and pinched sectional curvature. In particular, the first result concerns with an upper bound of sectional curvature, improving a…
This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.
This paper has been withdrawn by the author due to a serious gap in the proof of the main theorem.
This paper has been withdrawn by the author due to a crucial sign error in equation (5).
An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe invariants of weighted projective spaces…
In this work we wish characterize the Einstein manifolds $(M,g)$, however without the necessity of hypothesis of compactness over $M$ and unitary volume of $g$, which are well known in many works. Our result says that if all eingenvalues…
This paper has been withdrawn by the authors due to a fatal flaw in the central proof.
Let (M, g) be a closed Riemannian manifold and gE the Euclidean metric. We show that for m > 1, (M x R^m, (g + gE)) is not conformal to a positive Einstein manifold. Moreover, (M x R^m, (g + gE)) is not conformal to a Riemannian manifold of…
Let $M=G/K$ be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group $G$. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also…
The paper has been withdrawn by change of content and some errors in the examples.
This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
This paper has been withdrawn by the author due to a serious flaw that needs to be fixed. That is in progress by the author.
Recall that the usual Einstein metrics are those for which the first Ricci contraction of the covariant Riemann curvature tensor is proportional to the metric. Assuming the same type of restrictions but instead on the different contractions…
We prove the existence of an abundance of new Einstein metrics on odd dimensional spheres including exotic spheres, many of them depending on continuous parameters. The number of families as well as the number of parameter grows double…
The existence or non-existence of Einstein metrics on 4-manifolds with non-trivial fundamental group and the relation with the underlying differential structure are analyzed. For most points $(n,m)$ in a large region of the integer lattice,…
This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.