Matsumoto Metrics of Constant Flag Curvature: A Puny Class of Finsler Metrics with Constant Curvature

2011 ◽  
Vol 63 (1-2) ◽  
pp. 475-483 ◽  
Author(s):  
M. Rafie-Rad ◽  
B. Rezaei
Keyword(s):  
Constant Curvature ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Constant Flag Curvature

On Finsler surfaces of constant curvature with two-dimensional isometry group

2015 ◽  
Vol 26 (07) ◽  
pp. 1550046
Author(s):  
Libing Huang ◽  
Xiaohuan Mo
Keyword(s):  
Constant Curvature ◽  
Isometry Group ◽  
Flag Curvature ◽  
New Technique ◽  
Finsler Metrics ◽  
Two Dimensional ◽  
Constant Flag Curvature ◽  
A New Technique

In this paper, we study Finsler surfaces of constant (flag) curvature. We show that the space of those, with two-dimensional isometric group depends on two arbitrary constants. We also give a new technique to recover Finsler metrics from the specified two constants. Using this technique we obtain some new Finsler surfaces of constant flag curvature with two-dimensional isometry group.

On a Class of Projectively Flat Metrics with Constant Flag Curvature

2008 ◽  
Vol 60 (2) ◽  
pp. 443-456 ◽  
Author(s):  
Z. Shen ◽  
G. Civi Yildirim
Keyword(s):  
Local Structure ◽  
Riemannian Metric ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Constant Flag Curvature ◽  
Projectively Flat

AbstractIn this paper, we find equations that characterize locally projectively flat Finsler metrics in the form , where is a Riemannian metric and is a 1-form. Then we completely determine the local structure of those with constant flag curvature.

ON A CLASS OF PROJECTIVELY FLAT FINSLER METRICS WITH CONSTANT FLAG CURVATURE

2007 ◽  
Vol 18 (07) ◽  
pp. 749-760 ◽  
Author(s):  
BENLING LI ◽  
ZHONGMIN SHEN
Keyword(s):  
Riemannian Metric ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Constant Flag Curvature ◽  
Projectively Flat

In this paper, we study a class of Finsler metrics defined by a Riemannian metric and a 1-form. We classify those projectively flat with constant flag curvature.

scholarly journals A Local Classification of Some Special (α,β)-Metrics of Constant Flag Curvature

Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hongmei Zhu
Keyword(s):  
Flag Curvature ◽  
Finsler Metrics ◽  
Constant Flag Curvature ◽  
Local Classification

We classify some special Finsler metrics of constant flag curvature on a manifold of dimension n>2.

scholarly journals Randers manifolds of positive constant curvature

2003 ◽  
Vol 2003 (18) ◽  
pp. 1155-1165 ◽  
Author(s):  
Aurel Bejancu ◽  
Hani Reda Farran
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Positive Constant ◽  
Complete Riemannian Manifold ◽  
Flag Curvature ◽  
Dimensional Sphere ◽  
Randers Metric ◽  
Constant Flag Curvature ◽  
Simply Connected

We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odd-dimensional sphere, provided a certain 1-form vanishes on it.

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