scholarly journals There exist no locally symmetric Finsler spaces of positive or negative flag curvature

2015 ◽  
Vol 353 (1) ◽  
pp. 81-83
Author(s):  
Vladimir S. Matveev
Keyword(s):  
Flag Curvature ◽  
Finsler Spaces

On Flag Curvature of Homogeneous Randers Spaces

2013 ◽  
Vol 65 (1) ◽  
pp. 66-81 ◽  
Author(s):  
Shaoqiang Deng ◽  
Zhiguang Hu
Keyword(s):  
Explicit Formula ◽  
Lie Group ◽  
Flag Curvature ◽  
Nilpotent Lie Group ◽  
Finsler Spaces ◽  
Rigidity Result ◽  
Randers Space ◽  
Negatively Curved

AbstractIn this paper we give an explicit formula for the flag curvature of homogeneous Randers spaces of Douglas type and apply this formula to obtain some interesting results. We first deduce an explicit formula for the flag curvature of an arbitrary left invariant Randersmetric on a two-step nilpotent Lie group. Then we obtain a classification of negatively curved homogeneous Randers spaces of Douglas type. This results, in particular, in many examples of homogeneous non-Riemannian Finsler spaces with negative flag curvature. Finally, we prove a rigidity result that a homogeneous Randers space of Berwald type whose flag curvature is everywhere nonzero must be Riemannian.

Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ming Xu
Keyword(s):  
Lie Algebra ◽  
Finsler Space ◽  
Finsler Manifold ◽  
Constant Speed ◽  
Flag Curvature ◽  
Finsler Metric ◽  
Coset Space ◽  
Finsler Spaces ◽  
Negatively Curved ◽  
Positively Curved

Abstract We study the interaction between the g.o. property and certain flag curvature conditions. A Finsler manifold is called g.o. if each constant speed geodesic is the orbit of a one-parameter subgroup. Besides the non-negatively curved condition, we also consider the condition (FP) for the flag curvature, i.e. in any flag we find a flag pole such that the flag curvature is positive. By our main theorem, if a g.o. Finsler space (M, F) has non-negative flag curvature and satisfies (FP), then M is compact. If M = G/H where G has a compact Lie algebra, then the rank inequality rk 𝔤 ≤ rk 𝔥+1 holds. As an application,we prove that any even-dimensional g.o. Finsler space which has non-negative flag curvature and satisfies (FP) is a smooth coset space admitting a positively curved homogeneous Riemannian or Finsler metric.

On projective invariants of spherically symmetric Finsler spaces in Rn

2015 ◽  
Vol 12 (07) ◽  
pp. 1550074 ◽  
Author(s):  
Nasrin Sadeghzadeh ◽  
Maedeh Hesamfar
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finsler Spaces ◽  
Projective Invariants ◽  
Necessary And Sufficient

In this paper, we study projective invariants of spherically symmetric Finsler metrics in Rn. We find the necessary and sufficient conditions for the metrics to be Weyl, Douglas and generalized Douglas–Weyl (GDW) types. In particular, we find the necessary and sufficient condition for the metrics to be of scalar flag curvature. Also we show that two classes of GDW and Douglas spherically symmetric Finsler metrics coincide.

scholarly journals Even dimensional homogeneous Finsler spaces with positive flag curvature

2017 ◽  
Vol 66 (3) ◽  
pp. 949-972 ◽  
Author(s):  
Shaoqiang Deng ◽  
Ming Xu ◽  
Libing Huang ◽  
Zhiguang Hu
Keyword(s):  
Flag Curvature ◽  
Finsler Spaces ◽  
Positive Flag Curvature

scholarly journals On complete Finsler spaces of constant negative Ricci curvature

2020 ◽  
Vol 17 (03) ◽  
pp. 2050041
Author(s):  
Behroz Bidabad ◽  
Maryam Sepasi
Keyword(s):  
Ricci Curvature ◽  
Schwarzian Derivative ◽  
Finsler Space ◽  
Ricci Scalar ◽  
Flag Curvature ◽  
Finsler Spaces ◽  
Randers Metric

Here, using the projectively invariant pseudo-distance and Schwarzian derivative, it is shown that every connected complete Finsler space of the constant negative Ricci scalar is reversible. In particular, every complete Randers metric of constant negative Ricci (or flag) curvature is Riemannian.

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