49 citations · 73 across the 11 of their papers we have counts for
11 papers
Conformally Einstein Lorentzian Lie groups with Heisenberg symmetry
Esteban Calviño-Louzao, Eduardo Garcia-Rio, Ixchel Gutierrez-Rodriguez +1
We describe all Lorentzian semi-direct extensions of the Heisenberg group which are conformally Einstein. As a by side result, Bach-flat left-invariant Lorentzian metrics on semi-d…
Constructing Bach Flat Manifolds of signature using the modified Riemannian extension
E. Calviño-Louzao, E. García-Río, P. Gilkey +2
We use the modified Riemannian extension of an affine surface to construct Bach flat manifolds. As all these examples are VSI (vanishing scalar invariants), we shall construct scal…
Affine surfaces which are Kähler, para-Kähler, or nilpotent Kähler
E. Calviño-Louzao, E. García-Río, P. Gilkey +2
Motivated by the construction of Bach flat neutral signature Riemannian extensions, we study the space of parallel trace free tensors of type on an affine surface. It is sh…
Bach-flat isotropic gradient Ricci solitons
Esteban Calviño-Louzao, Eduardo García-Río, Ixchel Gutiérrez-Rodríguez +1
We construct examples of Bach-flat gradient Ricci solitons which are neither half conformally flat nor conformally Einstein.
Conformal geometry of non-reductive four-dimensional homogeneous spaces
E. Calviño-Louzao, E. García-Río, I. Gutiérrez-Rodríguez +1
We classify non-reductive four-dimensional homogeneous conformally Einstein manifolds.
Homogeneous Ricci almost solitons
E. Calviño-Louzao, M. Fernández-López, E. García-Río +1
It is shown that a locally homogeneous proper Ricci almost soliton is either of constant sectional curvature or a product , where is a space of consta…
Geometric properties of generalized symmetric spaces
E. Calviño-Louzao, E. García-Río, M. E. Vázquez-Abal +1
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an applic…
Homogeneous Cotton solitons
E. Calviño-Louzao, L. M. Hervella, J. Seoane-Bascoy +1
Left-invariant Cotton solitons on homogeneous manifolds are determined. Moreover, algebraic Cotton solitons are studied providing examples of non-invariant Cotton solitons, both in…
Three-dimensional conformally symmetric manifolds
E. Calviño-Louzao, E. García-Río, J. Seoane-Bascoy +1
The non-existence of non-trivial conformally symmetric manifolds in the three-dimensional Riemannian setting is shown. In Lorentzian signature, a complete local classification is o…
Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators
E. Calvino-Louzao, E. Garcia-Rio, P. Gilkey +1
We exhibit Osserman metrics with non-nilpotent Jacobi operators and with non-trivial Jordan normal form in neutral signature (n,n) for any n which is at least 3. These examples adm…
The geometry of modified Riemannian extensions
E. Calvino-Louzao, E. Garcia-Rio, P. Gilkey +1
We show that every paracomplex space form is locally isometric to a modified Riemannian extension and give necessary and sufficient conditions so that a modified Riemannian extensi…