Pinched Curvature in Heintze Groups of Carnot-type
Differential Geometry
2021-02-25 v4 Geometric Topology
Metric Geometry
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.
Keywords
Cite
@article{arxiv.2002.04594,
title = {Pinched Curvature in Heintze Groups of Carnot-type},
author = {Brendan Burns Healy},
journal= {arXiv preprint arXiv:2002.04594},
year = {2021}
}
Comments
Streamlined background and final sections