Distinguished G2-structures on solvmanifolds
Jorge Lauret
TL;DR
This paper investigates special classes of closed G2-structures on solvmanifolds, focusing on their existence, properties, and interrelations, with insights into Ricci pinching and extremal geometric features.
Contribution
It explores the existence and interplay of Laplacian solitons and Extremally Ricci-pinched G2-structures on solvable Lie groups, introducing new Ricci pinching properties.
Findings
Identified Ricci pinching properties of G2-structures on solvmanifolds.
Analyzed extremal points of the Ricci pinching functional.
Discussed open problems in the classification of G2-structures.
Abstract
Among closed G2-structures there are two very distinguished classes: Laplacian solitons and Extremally Ricci-pinched G2-structures. We study the existence problem and explore possible interplays between these concepts in the context of left-invariant G2-structures on solvable Lie groups. Also, some Ricci pinching properties of G2-structures on solvmanifolds are obtained, in terms of the extremal values and points of the Ricci pinching functional F=scal/|Ric|. Many natural open problems have been included.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology