TARU PUBLICATIONS
Journal of Dynamical Systems and Geometric Theories cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

WoS  JIF 2026 : 0.5 (Q3)

Powered by:Powered by

Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

Issues up to 2022 co-published with and available at:Taylor & Francis
info@tarupublications.com
Open Access Article

On Spherically Symmetric Landsberg Metrics

pp. 71–81Vol. 17Issue 1January 2019DOI: 10.1080/1726037X.2018.1551718XML
Received:
23 Nov 2017
Accepted:
14 May 2018
Published Online:
16 May 2019
Article type:
Article
Language:
EN
Article no.:
1726037X.2018.1551718
Pages:
71–81

Abstract

In this paper, we have studied spherically symmetric Landsberg metrics with isotropic E-curvature and isotropic S-curvature. In the first case we have shown that the metric reduces to a Berwald metric and therefore, it is of vanishing E-curvature. In the second case we have completely classified the spherically symmetric Landsberg metric with isotropic S-curvature.

Keywords

Subject Classifications

53B4053B50

References

  1. D.Bao, On two curvature-driven problems in Finsler geometry , Adv. Study Pure Math , Vol. 48 , 19 - 71 ( 2007 ).
  2. D.Bao, S.S.Chern and Z.Shen, An Introduction to Riemann-Finsler Geometry, 200, Graduate Texts in Math. Springer-Verlag, New York, 2000 .
  3. X.Chen and Z.Shen, Randers metric with special curvature properties , Osaka J. Math ., Vol. 40 , 87 - 101 ( 2003 ).
  4. Y.Chen and W.Song, Spherically Symmetric Finsler Metrics with Isotropic -curvature , J. Math. Res. Appl ., Vol. 35 , Number 5 , 561 - 567 ( 2015 ).
  5. S.S.Chern and Z.Shen, Riemannian-Finsler geometry , World Scientific Publisher , Singapore, 2005 .
  6. M.Matsumoto, On Finsler spaces with Randers’ metric and special forms of important tensors , J. Math. Kyoto Univ ., Vol. 14 , Number 3 , 477 - 498 ( 1974 ).
  7. X.Mo and L.Zhou, The Curvature of Spherically Symmetric Finsler Metrics in R , arXiv:1202.4534v4 .
  8. G.Randers, On an Asymmetrical Metric in the Four-Space of General Relativity , Physical Review , Vol. 59 , ( 1941 ).
  9. S.F.Rutz, Symmetry in Finsler spaces , Contemp. Math ., Vol. 196 , 289 - 300 ( 1996 ).
  10. Y.Q.Yun, An introduction to general relativity (in chinese) , Peking University Press , 1987 .
  11. S.S.Chern, Finsler geometry is just Riemannian geometry without the quadratic restriction , Notices Amer. Math. Soc ., Vol. 43 , 959 - 963 ( 1996 ).
  12. Z.Shen, On some non-Riemannian quantities in Finsler geometry , Canad. Math. Bull ., Vol. 56 , 184 - 193 ( 2013 ).
  13. Z.Shen, Volume comparison and its applications in Riemann-Finsler geometry , Adv. Math ., Vol. 128 , 306 - 328 ( 1997 ).
  14. L.Zhou, The spherically symmetric Finsler metrics with isotropic -curature , J. Math. Anal. Appl ., Vol. 431 , 1008 - 1021 ( 2015 ).
Views: 36Downloads: 66Citations: 0