6 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…
On the Geometry of -Static Perfect Fluid Space-Times
Letizia Branca, Giulio Colombo, Paolo Mastrolia +2
In this paper we study the geometry of -static perfect fluid space-times (-SPFST, for short). In the context of Einstein's General Relativity, they arise from a space-time wh…
Some geometric properties of generalized -vacuum static spaces
Letizia Branca, Paolo Mastrolia, Marco Rigoli
In this paper we study the geometry of generalized -vacuum static spaces, proving estimates for the -scalar curvature and for the first eigenvalue of the Jacobi operator, and…
Some isolation and stability results for Einstein manifolds
Letizia Branca, Klaus Kroencke
We prove new isolation and stability results for Einstein manifolds in a variety of settings. Imposing conditions on the Weyl tensor, we establish new stability criteria for compac…
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…