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.

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 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.

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.

scholarly journals On Projectively Flat Finsler Warped Product Metrics of Constant Flag Curvature

2021 ◽  
Author(s):  
Huaifu Liu ◽  
Xiaohuan Mo
Keyword(s):  
Warped Product ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Product Metrics ◽  
Constant Flag Curvature ◽  
Projectively Flat ◽  
Spherically Symmetric Metric

AbstractIn this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these metrics by warped product. Using the obtained equations, we manufacture new locally projectively flat Finsler warped product metrics of vanishing flag curvature. These metrics contain the metric introduced by Berwald and the spherically symmetric metric given by Mo-Zhu.

Sign in / Sign up

Export Citation Format

Share Document