• Corpus ID: 211075995

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}
}
  • B. Healy
  • Published 11 February 2020
  • Mathematics
  • arXiv: Differential Geometry
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… 

References

SHOWING 1-10 OF 37 REFERENCES
4-step Carnot spaces and the 2-stein condition
We consider the 2-stein condition on k-step Carnot spaces S. These spaces are a subclass in the class of solvable Lie groups of Iwasawa type of algebraic rank one and contain the homogeneous Einstein
A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms
The geometry of filiform nilpotent Lie groups
We study the geometry of a filiform nilpotent Lie group endowed with a leftinvariant metric. We describe the connection and curvatures, and we investigate necessary and sufficient conditions for
Pinching estimates for negatively curved manifolds with nilpotent fundamental groups
Abstract.Let M be a complete Riemannian metric of sectional curvature within [−a2,−1] whose fundamental group contains a k-step nilpotent subgroup of finite index. We prove that a ≥ k answering a
Three-step Harmonic Solvmanifolds
The Lichnerowicz conjecture asserted that every harmonic Riemannian manifold is locally isometric to a two-point homogeneous space. In 1992, E. Damek and F. Ricci produced a family of
Isometry groups of homogeneous quaternionic Kähler manifolds
AbstractA general method for calculation of the full isometry group of a Riemannian solvmanifold is presented.Using it we determine the full isometry group of the non-symmetric quaternionic Kähler
Contracting automorphisms and Lp-cohomology in degree one
We characterize those Lie groups, and algebraic groups over a local field of characteristic zero, whose first reduced Lp-cohomology is zero for all p>1, extending a result of Pansu. As an
Metric Spaces of Non-Positive Curvature
This book describes the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by
On the quasi-isometric classification of locally compact groups
This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of
Separated Nets in Nilpotent Groups
In this paper we generalize several results on separated nets in Euclidean space to separated nets in connected simply connected nilpotent Lie groups. We show that every such group $G$ contains
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3
4
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