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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
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri:For a certain Riemannian metric h; i, the Levi-Civitaconnection and the sectional curvature are given.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

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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Bu Makaleye Atıf Yap

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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Kaynakça (10)

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  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 (; )-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). Proc. Am. Math. Soc. 119 (1993), 611-619.