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 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.

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 Some Explicit Constructions of Finsler Metrics with Scalar Flag Curvature

2010 ◽  
Vol 62 (6) ◽  
pp. 1325-1339 ◽  
Author(s):  
Xiaohuan Mo ◽  
Changtao Yu
Keyword(s):  
Explicit Construction ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Arbitrary Degree ◽  
Constant Flag Curvature ◽  
Projectively Flat ◽  
Explicit Constructions

AbstractWe give an explicit construction of polynomial (of arbitrary degree) (α, β)-metrics with scalar flag curvature and determine their scalar flag curvature. These Finsler metrics contain all nontrivial projectively flat (α, β)-metrics of constant flag curvature.

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

2013 ◽  
Vol 24 (10) ◽  
pp. 1350087 ◽  
Author(s):  
GUOJUN YANG
Keyword(s):  
Real World ◽  
Local Structure ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
The Real ◽  
Constant Flag Curvature ◽  
Projectively Flat

Singular Finsler metrics, such as Kropina metrics and m-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular (α, β)-metrics which are locally projectively flat with constant flag curvature in dimension n = 2 and n ≥ 3 respectively. Further, we determine the local structure of m-Kropina metrics and particularly Kropina metrics which are projectively flat with constant flag curvature and prove that such metrics must be locally Minkowskian but are not necessarily flat-parallel.

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

2012 ◽  
Vol 23 (08) ◽  
pp. 1250084 ◽  
Author(s):  
XIAOHUAN MO ◽  
HONGMEI ZHU
Keyword(s):  
Structure Theorem ◽  
Finsler Geometry ◽  
Flag Curvature ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Constant Flag Curvature ◽  
Projectively Flat ◽  
Slight Generalization ◽  
Negative Constant ◽  
World Scientific Publishing

In this paper, we prove a structure theorem for projectively flat Finsler metrics of negative constant flag curvature. We show that for such a Finsler metric if the orthogonal group acts as isometries, then the Finsler metric is a slight generalization of Chern–Shen's construction Riemann–Finsler geometry, Nankai Tracts in Mathematics, Vol. 6 (World Scientific Publishing, Hackensack, NJ, 2005), x+192 pp.

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