5 papers · 1 filter
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…
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 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…