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Journals / International Electronic Journal of Geometry / 2019 / Volume: 12 Issue: 2

On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, r)

Masumeh Nejadahmad
Hamid Reza Salimi Moghaddam
Pages
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Publication Date
2019-10-03
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We classify all left invariant Randers metrics of Douglas type induced by h·, ·i, compute their flag curvatures and show that all of them are nonBerwaldian.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper we study the Riemann-Finsler geometry of the Lie groups H(p, r) which are a generalization of the Heisenberg Lie groups.
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Key Findings & Data:For a certain Riemannian metric h·, ·i, the Levi-Civita connection and the sectional curvature are given.
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Conclusion & Impact:We classify all left invariant Randers metrics of Douglas type induced by h·, ·i, compute their flag curvatures and show that all of them are nonBerwaldian.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:(α ¸ β)-metric · left invariant Finsler metric · left invariant Riemannian metric

Abstract

In this paper we study the Riemann-Finsler geometry of the Lie groups H(p, r) which are a generalization of the Heisenberg Lie groups. For a certain Riemannian metric h·, ·i, the Levi-Civita connection and the sectional curvature are given. We classify all left invariant Randers metrics of Douglas type induced by h·, ·i, compute their flag curvatures and show that all of them are nonBerwaldian.

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Cite This Article

Nejadahmad, M., Moghaddam, H. R. S. (2019). On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, r). International Electronic Journal of Geometry, Volume: 12 Issue: 2. https://doi.org/10.36890/iejg.628086

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References (10)

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