scholarly journals Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties

2007 ◽  
Vol 131 (1) ◽  
pp. 87-97 ◽  
Author(s):  
B. Najafi ◽  
Z. Shen ◽  
A. Tayebi
Keyword(s):  
Flag Curvature ◽  
Finsler Metrics ◽  
Riemannian Curvature

scholarly journals A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY

2012 ◽  
Vol 54 (3) ◽  
pp. 637-645 ◽  
Author(s):  
XIAOHUAN MO ◽  
ZHONGMIN SHEN ◽  
HUAIFU LIU
Keyword(s):  
Scalar Curvature ◽  
Simple Proof ◽  
Finsler Geometry ◽  
Finsler Manifold ◽  
Flag Curvature ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Riemannian Curvature

AbstractIn this note, we study a new Finslerian quantity Ĉ defined by the Riemannian curvature. We prove that the new Finslerian quantity is a non-Riemannian quantity for a Finsler manifold with dimension n = 3. Then we study Finsler metrics of scalar curvature. We find that the Ĉ-curvature is closely related to the flag curvature and the H-curvature. We show that Ĉ-curvature gives, a measure of the failure of a Finsler metric to be of weakly isotropic flag curvature. We also give a simple proof of the Najafi-Shen-Tayebi' theorem.

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.

Finsler Metrics with K = 0 and S = 0

2003 ◽  
Vol 55 (1) ◽  
pp. 112-132 ◽  
Author(s):  
Zhongmin Shen
Keyword(s):  
Euclidean Space ◽  
Shortest Path ◽  
External Force ◽  
Riemannian Space ◽  
Shortest Path Problem ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Randers Metric ◽  
Randers Space ◽  
Time Problem

AbstractIn the paper, we study the shortest time problem on a Riemannian space with an external force. We show that such problem can be converted to a shortest path problem on a Randers space. By choosing an appropriate external force on the Euclidean space, we obtain a non-trivial Randers metric of zero flag curvature. We also show that any positively complete Randers metric with zero flag curvature must be locally Minkowskian.

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.

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