ISSN 0253-2778

CN 34-1054/N

open
Free to Publish. Free to Read.
Open AccessOpen Access JUSTC Research Articles:Mathematics

A new class of projectively flat Finsler metrics

  • School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China

Funds:  Supported by the Anhui Normal University Graduate Student Research Innovation and Practical Projects (2015cxsj108zd), the National Natural Science Foundation of China (11071005).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.12.008
More Information
  • Author Bio:

    LI Ying, female, born in 1991, master. Research field: differential geometry. E-mail: 909789714@qq.com

  • Corresponding author: SONG Weidong
  • Received Date: 23 April 2015
  • Accepted Date: 25 September 2015
  • Rev Recd Date: 25 September 2015
  • Publish Date: 30 December 2015
    Abstract

  • Abstract

    A class of projectively flat Finsler metrics with three parameters was constructed, which generalizes a result obtained by Mo and Yang.

    Abstract

    A class of projectively flat Finsler metrics with three parameters was constructed, which generalizes a result obtained by Mo and Yang.
    • FullText(HTML)
  • loading
    • References(14)
  • [1]
    Hilbert D.Mathematical problems[J]. Bull Amer Math Soc, 2001, 37: 407-436.
    [2]
    Hamel G. Uber die Geometrieen in denen die Geraden die Kürzesten sind[J]. Math Ann, 1903,57: 231-264.
    [3]
    Mo X, Yu C. On some explicit constructions of Finsler metrics with scalar flag curvature[J]. Canad J Math, 2010, 62: 1 325-1 339.
    [4]
    Katok A. Ergodic perturbations of degenerate integrable Hamiltonian systems[J]. Lzv Akad Nauk SSSR,1973, 37: 539-576.
    [5]
    Bao D, Shen Z. Finsler metrics of constant positive curvature on the lie group S3[J]. J London Math Soc, 2002, 66: 453-467.
    [6]
    Shen Z. Finsler metrics with K=0 and S=0[J]. Canad J Math, 2003, 55: 112-132.
    [7]
    Bryant R.Finsler structures on the 2-spheres of constant curvature[J]. Selecta Math (NS), 1997,3: 161-204.
    [8]
    Mo X, Yang C. The explicit construction of Finsler metrics with special curvature properties[J]. Diff Geom Appl, 2006, 24: 119-121.
    [9]
    Song W, Zhou F. Spherically symmetric Finsler metrics with scalar flag curvature[J]. Turk J Math, 2015, 39: 16-22.
    [10]
    Mo X.On some projectively at Finsler metrics in terms of hypergeometric functions[J]. Israel Journal of Mathematics, 2011, 184: 59-78.
    [11]
    Bao D, Chern S, Shen Z. An Introduction to Riemann Finsler Geometry[M]. New York: Springer, 2000.
    [12]
    Chen X, Shen Z. Projectively at Finsler metrics with almost isotropic S-curvature[J]. Acta Mathmatica Scientia, 2006, 26B: 307-313.
    [13]
    Shen Y, Zhao L. Some projectively at (α; β)-metrics[J]. Sci China Ser A: Math, 2006, 49: 838-851.
    [14]
    Xu B, Li B. On a class of projectively at Finsler metrics with flag curvature K=1[J]. Differential Geometry and Its Applications, 2013, 31: 524-532.
    • Supplements(0)
    • Related Articles
    • Track Citations
  • 加载中

Catalog

    |
    Get Citation
    PDF
    XML
    [1]
    Hilbert D.Mathematical problems[J]. Bull Amer Math Soc, 2001, 37: 407-436.
    [2]
    Hamel G. Uber die Geometrieen in denen die Geraden die Kürzesten sind[J]. Math Ann, 1903,57: 231-264.
    [3]
    Mo X, Yu C. On some explicit constructions of Finsler metrics with scalar flag curvature[J]. Canad J Math, 2010, 62: 1 325-1 339.
    [4]
    Katok A. Ergodic perturbations of degenerate integrable Hamiltonian systems[J]. Lzv Akad Nauk SSSR,1973, 37: 539-576.
    [5]
    Bao D, Shen Z. Finsler metrics of constant positive curvature on the lie group S3[J]. J London Math Soc, 2002, 66: 453-467.
    [6]
    Shen Z. Finsler metrics with K=0 and S=0[J]. Canad J Math, 2003, 55: 112-132.
    [7]
    Bryant R.Finsler structures on the 2-spheres of constant curvature[J]. Selecta Math (NS), 1997,3: 161-204.
    [8]
    Mo X, Yang C. The explicit construction of Finsler metrics with special curvature properties[J]. Diff Geom Appl, 2006, 24: 119-121.
    [9]
    Song W, Zhou F. Spherically symmetric Finsler metrics with scalar flag curvature[J]. Turk J Math, 2015, 39: 16-22.
    [10]
    Mo X.On some projectively at Finsler metrics in terms of hypergeometric functions[J]. Israel Journal of Mathematics, 2011, 184: 59-78.
    [11]
    Bao D, Chern S, Shen Z. An Introduction to Riemann Finsler Geometry[M]. New York: Springer, 2000.
    [12]
    Chen X, Shen Z. Projectively at Finsler metrics with almost isotropic S-curvature[J]. Acta Mathmatica Scientia, 2006, 26B: 307-313.
    [13]
    Shen Y, Zhao L. Some projectively at (α; β)-metrics[J]. Sci China Ser A: Math, 2006, 49: 838-851.
    [14]
    Xu B, Li B. On a class of projectively at Finsler metrics with flag curvature K=1[J]. Differential Geometry and Its Applications, 2013, 31: 524-532.
    Recommended articles
    TrendMD
    Volume 45 Issue 12 page: 1015-1022
    Cover

    Article Metrics

    Article views (33) PDF downloads(94)
    Proportional views

    Copyright © Editorial Office of JUSTC, All Rights Reserved. 皖ICP备05002528号

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return