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On a class of Finsler metrics with isotropic Berwald curvature

Hongmei Zhu
대한수학회 (The Korean Mathematical Society)|2017.03|대한수학회보 (Bulletin of the KMS)|제54권 제2호|pp. 399-416

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참고문헌

키워드

Finsler metricisotropic Berwald curvaturegeneral $\ab$-metric$S$-curvature
주제분류수학

초록

In this paper, we study a class of Finsler metrics called general $\ab$-metrics, which are defined by a Riemannian metric $\a$ and a $1$-form $\b$. We show that every general $\ab$-metric with isotropic Berwald curvature is either a Berwald metric or a Randers metric. Moreover, a lot of new isotropic Berwald general $\ab$-metrics are constructed explicitly.

Abstract

In this paper, we study a class of Finsler metrics called general $\ab$-metrics, which are defined by a Riemannian metric $\a$ and a $1$-form $\b$. We show that every general $\ab$-metric with isotropic Berwald curvature is either a Berwald metric or a Randers metric. Moreover, a lot of new isotropic Berwald general $\ab$-metrics are constructed explicitly.

참고문헌 (20)

  1. S. B´acs´o, "On Finsler spaces of Douglas type-a generalization of the notion of Berwald space", Publ. Math. Debrecen, 51(3-4), pp.385~406 (1997)
  2. D. Bao, "Zermelo navigation on Riemannian manifolds", J. Differential Geom, 66(3), pp.377~435 (2004)
  3. R. Bryant, "Some remarks on Finsler manifolds with constant flag curvature", Houston J. Math, 28(2), pp.221~262 (2002)
  4. X. Chen, "On the flag curvature of Finsler metrics of scalar curva-ture", J. London Math. Soc, 68(3), pp.762~780 (2003)
  5. X. Chen, "Randers metrics with special curvature properties", Osaka J. Math, 40(1), pp.87~101 (2003)
  6. X. Chen, "On Douglas metrics", Publ. Math. Debreen, 66, pp.503~512 (2007)
  7. X. Cheng, "A class of Finsler metrics with isotropic S-curvature", Israel J. Math, 169, pp.317~340 (2009)
  8. X. Cheng, "Einstein (α,β)-metrics", Israel J. Math, 192(1), pp.221~249 (2012)
  9. S. S. Chern, "Riemann-Finsler Geometry", pp.192~ (2005), World Scientific Publishing
  10. E. Guo, "On spherically symmetric Finsler metrics with isotropic Berwald curvature", Int. J. Geom. Methods Mod. Phys, 10(10), pp.13~ (2013)
  11. B. Li, "Projectively flat fourth root Finsler metrics", Can. Math. Bull, 55(1), pp.138~145 (2012)
  12. X. Mo, "On a class of projectively flat Finsler metrics of negative constant flag curvature", Internat. J. Math, 23(8), pp.14~ (2012)
  13. Z. Shen, "Diffierential Geometry of Spray and Finsler Spaces" (2001), Kluwer Academic Pub-lishers
  14. Z. Shen, "On a class of Einstein Finsler metrics", Internat. J. Math, 25(4), pp.18~ (2014)
  15. A. Tayebi, "On isotropic Berwald metric", Ann. Polon. Math, 103(2), pp.109~121 (2012)
  16. A. Tayebi, "S-curvature of isotropic Berwald metrics", Sci. China Ser. A, 51(12), pp.2198~2204 (2008)
  17. C. Yu, "On a new class of Finsler metrics", Differential Geom. Appl, 29(2), pp.244~254 (2011)
  18. C. Yu, "Projectively flat general (α, β)-metrics with constant flag curvature", J. Math. Anal. Appl, 429(2), pp.1222~1239 (2015)
  19. H. Zhu, "A class of Finsler metrics of scalar flag curvature", Differntial Geom. Appl, 40, pp.321~331 (2015)
  20. H. Zhu, "On general (α,β)-metrics with vanishing Douglas curvature", Internat. J. Math, 26(9), pp.16~ (2015)

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