SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

On Homogeneous Randers Metrics

Akbar SADIGHI
Megerdich TOOMANIAN
Behzad NAJAFI
Pages
217–225
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

This provides an extension of well-known Deng-Hu theorem that proves the same result for a homogeneous Berwald-Randers metric of non-zero flag curvature.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the curvature features of the class of homogeneous Randers metrics.
📊
Key Findings & Data:For these metrics, we first find a reduction criterion to be a Berwald metric based on a mild restriction on their Ricci tensors.
💡
Conclusion & Impact:This provides an extension of well-known Deng-Hu theorem that proves the same result for a homogeneous Berwald-Randers metric of non-zero flag curvature.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Homogeneous metric · Homogeneous metric · Ricci tensor

Abstract

In this paper, we study the curvature features of the class of homogeneous Randers metrics. For these metrics, we first find a reduction criterion to be a Berwald metric based on a mild restriction on their Ricci tensors. Then, we prove that every homogeneous Randers metric with relatively isotropic (or weak) Landsberg curvature must be Riemannian. This provides an extension of well-known Deng-Hu theorem that proves the same result for a homogeneous Berwald-Randers metric of non-zero flag curvature.

🔖

Cite This Article

SADIGHI, A., TOOMANIAN, M., NAJAFI, B. (2022). On Homogeneous Randers Metrics. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 217–225. https://ajindex.com/articles/539562

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. H. Akbar-Zadeh, Generalized Einstein manifolds, Jour. Geom. Phys. 17(1995), 342- 380
  2. D. Bao, On two curvature-driven problems in Finsler geometry, Adv. Study Pure Math, 48(2007), Finsler Geometry, Sapporo 2005 - In Memery of Makoto Mat- sumoto, 19-71
  3. D. Bao and C. Robles, Ricci and Flag curvatures in Finsler geometry, A Sampler of Riemann-Finlser Geometry, MSRIP. 50(2004), 198-256
  4. L. Berwald, Über Parallelübertragung in Raumen mit allgemeiner Massbestimmung,Jber. Deutsch. Math.-Verein, 34(1925), 213-220
  5. S. Deng and Z. Hou, The group of isometries of a Finsler space, Pacific. J. Math, 207(2002), 149-155
  6. S. Deng and Z. Hou, Homogeneous Einstein-Randers spaces of negative Ricci curva- ture, C. R. Math. Acad. Sci. Paris. 347(2009), 1169-1172
  7. S. Deng and Z. Hu, Curvatures of homogeneous Randers spaces, Adv. Math. 240(2013), 194-226
  8. S. Deng and Z. Hu, On flag curvature of homogeneous Randers spaces, Canad. J. Math. 65(2013), 66-81
  9. E. Esrafilian and H.R. Salimi Moghaddam, Flag curvature of invariant Randers metrics on homogeneous manifolds, J. Phys. A: Math. Gen. 39(2006), 3319-3324
  10. Z. Hu and S. Deng, Ricci-quadratic homogeneous Randers spaces, Nonlinear Analysis. 92(2013), 130-137
  11. B. Li and Z. Shen, Ricci curvature tensor and non-Riemannian quantities, Canadian Mathematical Bulletin, 58(2015), 530-537
  12. M. Matsumoto, Foundations of Finsler Geometry and special Finsler Spaces, Kai- seisha Press, Japan 1986
  13. M. Matsumoto, An improvment proof of Numata and Shibata’s theorem on Finsler spaces of scalar curvature, Publ. Math. Debrecen, 64(2004), 489-500
  14. G. Randers, On an asymmetric metric in the four-space of general relativity, Phys. Rev. 59(1941), 195-199
  15. C. Robles, Einstein metrics of Randers type, Doctoral Dissertation, University of British Columbia, 2003
  16. Z. Shen, Finsler metrics with K = 0 and S = 0, Canadian J. Math. 55(2003), 112-132
  17. Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Pub- lishers, 2001
  18. C. Shibata, On Finsler spaces with Kropina metrics, Report. Math., 13(1978), 117- 128
  19. H. Shimada, On the Ricci tensors of particular Finsler spaces, J. Korean Math. Soc. 14(1977), 41-63
  20. A. Tayebi and E. Peyghan, On Ricci tensors of Randers metrics, J. Geom. Phys. 60(2010), 1665-1670
  21. M. Xu and S. Deng, Homogeneous (α,β)-spaces with positive flag curvature and vanishing S-curvature, Nonlinear Analysis. 127(2015), 45-54.