Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2019, Cilt: 12 Sayı: 2, 218 - 222, 03.10.2019

Masumeh Nejadahmad Hamid Reza Salimi Moghaddam

https://doi.org/10.36890/iejg.628086

Öz

Kaynakça

  • [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.

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

Yıl 2019, Cilt: 12 Sayı: 2, 218 - 222, 03.10.2019

Masumeh Nejadahmad Hamid Reza Salimi Moghaddam

https://doi.org/10.36890/iejg.628086

Öz

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.

Anahtar Kelimeler

(α ¸ β)-metric left invariant Finsler metric left invariant Riemannian metric curvature nilpotent Lie group

Kaynakça

  • [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.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Masumeh Nejadahmad Bu kişi benim

Hamid Reza Salimi Moghaddam Bu kişi benim

Yayımlanma Tarihi 3 Ekim 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 2

Kaynak Göster

APA 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, 12(2), 218-222. https://doi.org/10.36890/iejg.628086
AMA Nejadahmad M, Moghaddam HRS. On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, r). Int. Electron. J. Geom. Ekim 2019;12(2):218-222. doi:10.36890/iejg.628086
Chicago Nejadahmad, Masumeh, ve Hamid Reza Salimi Moghaddam. “On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, R)”. International Electronic Journal of Geometry 12, sy. 2 (Ekim 2019): 218-22. https://doi.org/10.36890/iejg.628086.
EndNote Nejadahmad M, Moghaddam HRS (01 Ekim 2019) On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, r). International Electronic Journal of Geometry 12 2 218–222.
IEEE M. Nejadahmad ve H. R. S. Moghaddam, “On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, r)”, Int. Electron. J. Geom., c. 12, sy. 2, ss. 218–222, 2019, doi: 10.36890/iejg.628086.
ISNAD Nejadahmad, Masumeh - Moghaddam, Hamid Reza Salimi. “On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, R)”. International Electronic Journal of Geometry 12/2 (Ekim 2019), 218-222. https://doi.org/10.36890/iejg.628086.
JAMA Nejadahmad M, Moghaddam HRS. On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, r). Int. Electron. J. Geom. 2019;12:218–222.
MLA Nejadahmad, Masumeh ve Hamid Reza Salimi Moghaddam. “On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, R)”. International Electronic Journal of Geometry, c. 12, sy. 2, 2019, ss. 218-22, doi:10.36890/iejg.628086.
Vancouver Nejadahmad M, Moghaddam HRS. On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, r). Int. Electron. J. Geom. 2019;12(2):218-22.
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