Pinched Curvature in Heintze Groups of Carnot-type

2020/02/11 by Healy, Brendan Burns
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2002.04594

Abstract

Rank-one symmetric spaces carry a solvable group model which have a generalization to a larger class of Lie groups that are one-dimensional extensions of nilpotent groups. By examining some metric properties of these symmetric spaces, we motivate and prove the existence of analogous left-invariant, Riemannian metrics on Heintze groups of Carnot-type. These metrics adhere to certain natural curvature pinching properties, and we show in a special case that this pinching is optimal, appealing to a result of Belegradek and Kapovitch.

Related

• Metric Lie Groups. Carnot-Carathéodory spaces from the homogeneous viewpoint
• Ricci curvatures in Carnot groups
• Sub-Riemannian curvature of Carnot groups with rank-two distributions
• A metric characterization of Carnot groups
• Invertible Carnot Groups