# Metrics of Pinched Curvature on Heintze Spaces of Carnot-type

@article{Healy2020MetricsOP, title={Metrics of Pinched Curvature on Heintze Spaces of Carnot-type}, author={Brendan Burns Healy}, journal={arXiv: Differential Geometry}, year={2020} }

Rank-one symmetric spaces 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 metrics on Heintze spaces of Carnot-type. As an application of this construction, we see that Heintze spaces with H-metrics are of Iwasawa type, fail to have the Einstein condition, and admit a useful symmetric adjoint action. We also introduce the…

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