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Conformally weighted Einstein manifolds: the uniqueness problem
Miguel Brozos-Vázquez, Eduardo García-Río, Diego Mojón-Álvarez
We discuss smooth metric measure spaces admitting two weighted Einstein representatives of the same weighted conformal class. First, we describe the local geometries of such manifo…
The vacuum weighted Einstein field equations
M. Brozos-Vázquez, D. Mojón-Álvarez
On a spacetime endowed with a density function , we consider the vacuum weighted Einstein field equations: \[hρ-\operatorname{Hes}_h+Δh g=0.\] First, it is shown that th…
The vacuum weighted Einstein field equations on pr-waves
Miguel Brozos-Vázquez, Diego Mojón-Álvarez
We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes of dimension 4, where the underlying manifold i…
Four-dimensional homogeneous critical metrics for quadratic curvature functionals
M. Brozos-Vázquez, S. Caeiro-Oliveira, E. García-Río +1
We determine all homogeneous metrics which are critical for some quadratic curvature functional in dimension four.
Rigidity of weighted Einstein smooth metric measure spaces
Miguel Brozos-Vázquez, Diego Mojón-Álvarez
We study the geometric structure of weighted Einstein smooth metric measure spaces with weighted harmonic Weyl tensor. A complete local classification is provided, showing that eit…
Solutions to the affine quasi-Einstein equation for homogeneous surfaces
M. Brozos-Vázquez, E. García-Río, P. Gilkey +1
We examine the space of solutions to the affine quasi--Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitions, co…