KaydedilenlerDerginizi ekleyin

Dergiler / 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
Sayfa
218–222
Yayın Tarihi
2019-10-03
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri:For a certain Riemannian metric h·, ·i, the Levi-Civita connection and the sectional curvature are given.
💡
Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:(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.

🔖

Bu Makaleye Atıf Yap

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, Cilt: 12 - Sayı: 2, 218–222. https://ajindex.com/articles/672081

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (10)

  1. An H. and Deng S.,, Invariant (α, β)-metrics on homogeneous manifolds. Monatsh. Math. 154 (2008), 89-102
  2. Asanov G.S., Finsler Geometry, Relativity and Gauge Theories. D. Reidel Pubishing Company, Dordrecht, Holland, 1985
  3. Bacso S. and Matsumoto M., On Finsler spaces of Douglas type. A generalization of the notion of Berwald space. Publ. Math. Debrecen 51 (1997), 385-406
  4. Bao D., Chern S. S. and Shen Z., An Introduction to Riemann-Finsler Geometry. Springer, 2000
  5. Chern S. S. and Shen Z., Riemann-Finsler Geometry. World Scientific, Singapore, 2005
  6. Deng S., Homogeneous Finsler Spaces. Springer, New York, 2012
  7. Deng S., Hosseini M., Liu H. and Salimi Moghaddam H. R., On the left invariant (α, β)-metrics on some Lie groups. Houston J. Math. to appear
  8. Deng S. and Hu Z., On Flag Curvature of Homogeneous Randers Spaces. Canad. J. Math. 65 (2013), no. 1, 66-81
  9. Goze M. and Haraguchi Y., Sur les r-systemes de contact. C. R. Acad. Sci. Paris Ser. I Math. 294 (1982), 95-97
  10. Piu P. and Goze M., On the Riemannian geometry of the nilpotent groups H(p, r (1993), 611-619.