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Journals / International Electronic Journal of Geometry / 2019 / Cilt: 12 - Sayı: 2

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

Masumeh NEJADAHMAD
Hamid Reza Salimi MOGHADDAM
Pages
218–222
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We classify all left invariant Randers metrics ofDouglas type induced by h; i, compute their flag curvatures and show that all of them are non-Berwaldian.

📌 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 ageneralization of the Heisenberg Lie groups.
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Key Findings & Data:For a certain Riemannian metric h; i, the Levi-Civitaconnection and the sectional curvature are given.
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Conclusion & Impact:We classify all left invariant Randers metrics ofDouglas type induced by h; i, compute their flag curvatures and show that all of them are non-Berwaldian.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

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

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Cite This Article

NEJADAHMAD, M., MOGHADDAM, H. R. S. (2022). On the Geometry of Some (α,β )-Metrics on the Nilpotent Groups H(p,r). International Electronic Journal of Geometry, Cilt: 12 - Sayı: 2, 218–222. https://ajindex.com/articles/539645

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References (10)

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