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Finsler metrics with reversible geodesics

Qiaoling Xia
대한수학회 (The Korean Mathematical Society)|2020.11|대한수학회보 (Bulletin of the KMS)|제57권 제6호|pp. 1335-1349|DOI 10.4134/BKMS.b181086

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키워드

Finsler metricgeneral $(\alpha\beta)$-metricreversible geodesic
주제분류수학

초록

In this paper, we give an equivalent characterization for general $(\alpha, \beta)$-metrics with reversible geodesics when the dimension of the manifold is greater than $2$.

Abstract

In this paper, we give an equivalent characterization for general $(\alpha, \beta)$-metrics with reversible geodesics when the dimension of the manifold is greater than $2$.

참고문헌 (12)

  1. D. Bao, "An introduction to Riemann-Finsler geometry" (2000), Springer-Verlag
  2. R. L. Bryant, "Projectively flat Finsler 2-spheres of constant curvature", Selecta Mathematica, 3(2), pp.161~203 (1997), Springer Science and Business Media LLC[DOI]
  3. R. L. Bryant, "Inspired by S. S. Chern", pp.95~111 (2006), World Sci. Publ
  4. S. -S. Chern, "Riemann-Finsler geometry" (2005), World Scientific Publishing Co. Pte. Ltd
  5. M. Crampin, "Randers spaces with reversible geodesics", Publ. Math. Debrecen, 67(3-4), pp.401~409 (2005)
  6. Yali Feng, "On a class of locally projectively flat Finsler metrics (II)", Differential Geometry and its Applications, 62, pp.39~59 (2019), Elsevier BV[DOI]
  7. IOANA MONICA MASCA, "REVERSIBLE GEODESICS FOR (α, β)-METRICS", International Journal of Mathematics, 21(08), pp.1071~1094 (2012), World Scientific Pub Co Pte Lt[DOI]
  8. IOANA M. MASCA, "Two dimensional $(\alpha,\beta)$-metrics with reversible geodesics", Publicationes Mathematicae Debrecen, 82(2), pp.485~501 (2013), University of Debrecen[DOI]
  9. Xiaohuan Mo, "On a class of locally projectively flat general (α, β)-metrics", 대한수학회보, 54(4), pp.1293~1307 (2017), 대한수학회
  10. Qiaoling Xia, "On a class of projectively flat Finsler metrics", Differential Geometry and its Applications, 44, pp.1~16 (2016), Elsevier BV[DOI]
  11. Qiaoling Xia, "On a Class of Finsler Metrics of Scalar Flag Curvature", Results in Mathematics, 71(1-2), pp.483~507 (2017), Springer Science and Business Media LLC[DOI]
  12. Changtao Yu, "On a new class of Finsler metrics", Differential Geometry and its Applications, 29(2), pp.244~254 (2011), Elsevier BV[DOI]

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