38 citations · 41 across the 9 of their papers we have counts for
11 papers
The mean curvature flow of subgroups on Lie groups of dimension three
Romina M. Arroyo, Gabriela P. Ovando, Mariel Sáez
In this work we study the existence of solutions to the Mean Curvature Flow for which the initial condition has the structure of a two-dimensional Lie subgroup within a Lie group o…
The mean curvature flow on solvmanifolds
Romina M. Arroyo, Gabriela P. Ovando, Raquel Perales +1
This work is a survey of the most relevant background material to motivate and understand the construction and classification of translating solutions to mean curvature flow on a f…
SKT structures on nilmanifolds
Romina M. Arroyo, Marina Nicolini
The aim of this article is to study the existence of invariant SKT structures on nilmanifolds. More precisely, we give a negative answer to the question of whether there exist a $k…
On the signature of the Ricci curvature on nilmanifolds
Romina M. Arroyo, Ramiro A. Lafuente
We completely describe the signatures of the Ricci curvature of left-invariant Riemannian metrics on arbitrary real nilpotent Lie groups. The main idea in the proof is to exploit a…
The prescribed Ricci curvature problem for naturally reductive metrics on non-compact simple Lie groups
Romina M. Arroyo, Mark D. Gould, Artem Pulemotov
We investigate the prescribed Ricci curvature problem in the class of left-invariant naturally reductive Riemannian metrics on a non-compact simple Lie group. We obtain a number of…
The prescribed Ricci curvature problem for naturally reductive metrics on compact Lie groups
Romina M. Arroyo, Artem Pulemotov, Wolfgang Ziller
We study the problem of prescribing the Ricci curvature in the class of naturally reductive metrics on a compact Lie group. We derive necessary as well as sufficient conditions for…
The long-time behavior of the homogeneous pluriclosed flow
Romina M. Arroyo, Ramiro A. Lafuente
We study the asymptotic behavior of the pluriclosed flow in the case of left-invariant Hermitian structures on Lie groups. We prove that solutions on 2-step nilpotent Lie groups an…
The Alekseevskii conjecture in low dimensions
Romina M. Arroyo, Ramiro A. Lafuente
The long-standing Alekseevskii conjecture states that a connected homogeneous Einstein space G/K of negative scalar curvature must be diffeomorphic to R^n. This was known to be tru…
Homogeneous Ricci solitons in low dimensions
Romina M. Arroyo, Ramiro Lafuente
In this article we classify expanding homogeneous Ricci solitons up to dimension 5, according to their presentation as homogeneous spaces. We obtain that they are all isometric to…
The Ricci flow in a class of solvmanifolds
Romina M. Arroyo
In this paper, we study the Ricci flow of solvmanifolds whose Lie algebra has an abelian ideal of codimension one, by using the bracket flow. We prove that solutions to the Ricci f…
Filiform nilsolitons of dimension 8
Romina M. Arroyo
A Riemannian manifold (M,g) is said to be Einstein if its Ricci tensor satisfies ric(g) = cg, for some real number c. In the homogeneous case, a problem that is still open is the s…