NEW TOOLS IN FINSLER GEOMETRY: STRETCH AND RICCI SOLITONS

被引：0
|
作者：
Crasmareanu, Mircea [1 ]
机构：
[1] Alexandru Ioan Cuza Univ, Fac Math, Iasi 700506, Romania
来源：
MATHEMATICAL REPORTS | 2014年 / 16卷 / 01期
关键词：
Finsler (Minkowski) space stretch; reversibility; (alpha; beta)-metric; sphere theorem; Ricci soliton; Zermelo navigation problem; flag curvature; MANIFOLDS; METRICS; DILATATION; NAVIGATION; SPHERES;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Firstly, the notion of stretch from Riemannian geometry is extended to Finsler spaces in relationship with the smoothness function of Ohta and the reversibility function of Rademacher. As an application, the Sphere Theorem of Rademacher is rewritten in terms of stretch for the case of Randers and Matsumoto metrics by pointed out the usual Riemannian pinching constant 1/4. Secondly, one put in evidence a strong relationship, induced by the Zermelo navigation problem, between Randers metrics of constant flag curvature and Ricci solitons.
引用
收藏
页码：83 / 93
页数：11
相关论文
共 50 条
  • [21] On Some Ricci Curvature Tensors in Finsler Geometry
    Sevim, Esra Sengelen
    Shen, Zhongmin
    Ulgen, Semail
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (04)
  • [22] On Some Ricci Curvature Tensors in Finsler Geometry
    Esra Sengelen Sevim
    Zhongmin Shen
    Semail Ulgen
    Mediterranean Journal of Mathematics, 2023, 20
  • [23] WEIGHTED PROJECTIVE RICCI CURVATURE IN FINSLER GEOMETRY
    Tabatabaeifar, Tayebeh
    Najafi, Behzad
    Tayebi, Akbar
    MATHEMATICA SLOVACA, 2021, 71 (01) : 183 - 198
  • [24] Optimal transport and Ricci curvature in Finsler geometry
    Ohta, Shin-ichi
    PROBABILISTIC APPROACH TO GEOMETRY, 2010, 57 : 323 - 342
  • [25] Ricci Almost Solitons And Gradient Ricci Almost Solitons In (k, μ)-Paracontact Geometry
    De, U. C.
    Mandal, krishanu
    BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2019, 37 (03): : 119 - 130
  • [26] Geometry of compact shrinking Ricci solitons
    Chen, Bang Yen
    Deshmukh, Sharief
    BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, 2014, 19 (01): : 13 - 21
  • [27] Ricci almost solitons and contact geometry
    Ghosh, Amalendu
    ADVANCES IN GEOMETRY, 2021, 21 (02) : 169 - 178
  • [28] Twisted Ricci flow on a class of Finsler metrics and its solitons
    Shen, Bin
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2016, 46 : 132 - 145
  • [29] On conformal transformations preserving the Ricci tensor in Finsler geometry
    Shavakh, M. H.
    Bidabad, B.
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2024, 92
  • [30] Extrinsic Geometry of a Riemannian Manifold and Ricci Solitons
    Al-Dayel, Ibrahim
    Deshmukh, Sharief
    AXIOMS, 2025, 14 (02)
12345