scholarly journals On the Projective Algebra of Randers Metrics of Constant Flag Curvature

2011 ◽  
Author(s):  
Mehdi Rafie-Rad
Keyword(s):  
Flag Curvature ◽  
Constant Flag Curvature ◽  
Projective Algebra ◽  
Randers Metrics

scholarly journals RANDERS METRICS OF SCALAR FLAG CURVATURE

2009 ◽  
Vol 87 (3) ◽  
pp. 359-370 ◽  
Author(s):  
XINYUE CHENG ◽  
ZHONGMIN SHEN
Keyword(s):  
Flag Curvature ◽  
Finsler Metrics ◽  
Important Class ◽  
Constant Flag Curvature ◽  
Projectively Flat ◽  
Randers Metrics

AbstractWe study an important class of Finsler metrics, namely, Randers metrics. We classify Randers metrics of scalar flag curvature whose S-curvatures are isotropic. This class of Randers metrics contains all projectively flat Randers metrics with isotropic S-curvature and Randers metrics of constant flag curvature.

On almost contact Finsler structures

2020 ◽  
Vol 17 (08) ◽  
pp. 2050126
Author(s):  
Tayebeh Tabatabaeifar ◽  
Behzad Najafi ◽  
Mehdi Rafie-Rad
Keyword(s):  
Mild Condition ◽  
Finsler Manifold ◽  
Flag Curvature ◽  
Finsler Manifolds ◽  
Constant Flag Curvature ◽  
Berwald Space ◽  
Randers Metrics

We introduce almost contact and cosymplectic Finsler manifolds. Then, we characterize almost contact Randers metrics. It is proved that a cosymplectic Finsler manifold of constant flag curvature must have vanishing flag curvature. We prove that every cosymplectic Finsler manifold is a Landsberg space, under a mild condition. Finally, we show that a cosymplectic Finsler manifold is a Douglas space if and only if it is a Berwald space.

ON PROJECTIVELY RELATED RANDERS METRICS

2008 ◽  
Vol 19 (05) ◽  
pp. 503-520 ◽  
Author(s):  
YIBING SHEN ◽  
YAOYONG YU
Keyword(s):  
Riemannian Metrics ◽  
Flag Curvature ◽  
Constant Flag Curvature ◽  
Randers Metrics

In this paper, we prove that two Randers metrics are pointwise projectively related if and only if they have the same Douglas tensors and the corresponding Riemannian metrics are projectively related. Moreover, Randers metrics of constant flag curvature and Einstein–Randers metrics are considered.

A Note on Randers Metrics of Scalar Flag Curvature

2012 ◽  
Vol 55 (3) ◽  
pp. 474-486 ◽  
Author(s):  
Bin Chen ◽  
Lili Zhao
Keyword(s):  
Scalar Curvature ◽  
Three Dimensional ◽  
Constant Scalar Curvature ◽  
Flag Curvature ◽  
Projectively Flat ◽  
Randers Metrics

AbstractSome families of Randers metrics of scalar flag curvature are studied in this paper. Explicit examples that are neither locally projectively flat nor of isotropic S-curvature are given. Certain Randers metrics with Einstein α are considered and proved to be complex. Three dimensional Randers manifolds, with α having constant scalar curvature, are studied.

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