Projectively flat Randers metrics with constant flag curvature

2003 ◽  
Vol 325 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Zhongmin Shen
Keyword(s):  
Flag Curvature ◽  
Constant Flag Curvature ◽  
Projectively Flat ◽  
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.

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.

On some classes of projectively flat Finsler metrics with constant flag curvature

2020 ◽  
Vol 68 ◽  
pp. 101579
Author(s):  
Guocai Cai ◽  
Chunhui Qiu ◽  
Xiuling Wang
Keyword(s):  
Flag Curvature ◽  
Finsler Metrics ◽  
Constant Flag Curvature ◽  
Projectively Flat

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 Projectively flat Finsler manifolds with infinite dimensional holonomy

2015 ◽  
Vol 27 (2) ◽  
Author(s):  
Zoltán Muzsnay ◽  
Péter T. Nagy
Keyword(s):  
Lie Group ◽  
Holonomy Group ◽  
Finsler Manifold ◽  
Flag Curvature ◽  
Compact Lie Group ◽  
Finsler Manifolds ◽  
Infinite Dimensional ◽  
Constant Flag Curvature ◽  
Projectively Flat

AbstractRecently, we developed a method for the study of holonomy properties of non-Riemannian Finsler manifolds and obtained that the holonomy group cannot be a compact Lie group if the Finsler manifold of dimension >2 has non-zero constant flag curvature. The purpose of this paper is to move further, exploring the holonomy properties of projectively flat Finsler manifolds of non-zero constant flag curvature. We prove in particular that projectively flat Randers and Bryant–Shen manifolds of non-zero constant flag curvature have infinite dimensional holonomy group.

Projectively Flat Singular Square Metrics with Constant Flag Curvature

2020 ◽  
Vol 36 (6) ◽  
pp. 638-650
Author(s):  
Guang Zu Chen ◽  
Xin Yue Cheng
Keyword(s):  
Flag Curvature ◽  
Constant Flag Curvature ◽  
Projectively Flat

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.

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