9 papers
On the Bach tensor and quadratic curvature functionals
Letizia Branca, Davide Dameno
We study the critical points of a quadratic functional depending on the gradient of the Bach tensor on Riemannian four-manifolds, which generalize the Bach-flat condition. We show…
Conformal Kähler rigidity of Einstein four-manifolds
Giovanni Catino, Davide Dameno
For a compact, connected, oriented Einstein four-manifold, we prove that, if the largest eigenvalue of the self-dual Weyl curvature is everywhere simple, then, after at worst…
Topological and rigidity results for four-dimensional hypersurfaces in space forms
Davide Dameno, Aaron J. Tyrrell
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First,…
A note on Einstein metrics and Riemannian twistor spaces
Davide Dameno
Inspired by the problem of classifying Einstein manifolds with positive scalar curvature, we prove that an Einstein four-manifold whose associated twistor space has scalar curvatur…
Bach-pinched metrics on closed manifolds
Letizia Branca, Giovanni Catino, Davide Dameno
Exploiting the deformation method introduced by Aubin in his seminal work to construct constant negative scalar curvature metrics, we show the existence, on every closed manifold o…
Rigidity of Einstein manifolds with positive Yamabe invariant
Letizia Branca, Giovanni Catino, Davide Dameno +1
We provide optimal pinching results on closed Einstein manifolds with positive Yamabe invariant in any dimension, extending the optimal bound for the scalar curvature due to Gursky…
Rigidity results for Riemannian twistor spaces under vanishing curvature conditions
Giovanni Catino, Davide Dameno, Paolo Mastrolia
In this paper we provide new rigidity results for four-dimensional Riemannian manifolds and their twistor spaces.In particular, using the moving frame method, we prove that $\mathb…
Some canonical metrics {\em via} Aubin's local deformations
Giovanni Catino, Davide Dameno, Paolo Mastrolia
In this paper, using special metric deformations introduced by Aubin, we construct Riemannian metrics satisfying non-vanishing conditions concerning the Weyl tensor, on every compa…
On Riemannian four-manifolds and their twistor spaces: a moving frame approach
Giovanni Catino, Davide Dameno, Paolo Mastrolia
In this paper we study the twistor space of an oriented Riemannian four-manifold using the moving frame approach, focusing, in particular, on the Einstein, non-self-dual se…