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Year 2019, , 218 - 222, 03.10.2019

Masumeh Nejadahmad Hamid Reza Salimi Moghaddam

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

Abstract

References

  • [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)

Year 2019, , 218 - 222, 03.10.2019

Masumeh Nejadahmad Hamid Reza Salimi Moghaddam

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

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.

Keywords

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

References

  • [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.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Masumeh Nejadahmad This is me

Hamid Reza Salimi Moghaddam This is me

Publication Date October 3, 2019
Published in Issue Year 2019

Cite

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. October 2019;12(2):218-222. doi:10.36890/iejg.628086
Chicago Nejadahmad, Masumeh, and 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, no. 2 (October 2019): 218-22. https://doi.org/10.36890/iejg.628086.
EndNote Nejadahmad M, Moghaddam HRS (October 1, 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 and H. R. S. Moghaddam, “On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, r)”, Int. Electron. J. Geom., vol. 12, no. 2, pp. 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 (October 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 and Hamid Reza Salimi Moghaddam. “On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, R)”. International Electronic Journal of Geometry, vol. 12, no. 2, 2019, pp. 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.