Laplacian flow of homogeneous G 2 -structures and its solitons

• Autores: Lauret, Jorge Ruben
• Año de publicación: 2017
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: 53C44 (PRIMARY)
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

We use the bracket flow/algebraic soliton approach to study the Laplacian flow of G2-structures and its solitons in the homogeneous case. We prove that any homogeneous Laplacian soliton is equivalent to a semi-algebraic soliton (that is, a G-invariant G2-structure on a homogeneous space G/K that flows by pull-back of automorphisms of G up to scaling). Algebraic solitons are geometrically characterized among Laplacian solitons as those with a 'diagonal' evolution. Unlike the Ricci flow case, where any homogeneous Ricci soliton is isometric to an algebraic soliton, we have found, as an application of the above characterization, an example of a left-invariant closed semi-algebraic soliton on a nilpotent Lie group which is not equivalent to any algebraic soliton. The (normalized) bracket flow evolution of such a soliton is periodic. In the context of solvable Lie groups with a codimension-one abelian normal subgroup, we obtain long-time existence for any closed Laplacian flow solution; furthermore, the norm of the torsion is strictly decreasing and converges to zero. We also classify algebraic solitons in this class and exhibit several explicit examples of closed expanding Laplacian solitons.
Fil: Lauret, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina