scholarly journals The geometry of a positively curved Zoll surface of revolution

2019 ◽  
Vol 16 (supp02) ◽  
pp. 1941003 ◽  
Author(s):  
Kazuyoshi Kiyohara ◽  
Sorin V. Sabau ◽  
Kazuhiro Shibuya
Keyword(s):  
Gauss Curvature ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Surface Of Revolution ◽  
Constant Flag Curvature ◽  
Explicit Constructions ◽  
Positively Curved ◽  
Positive Gauss Curvature

In this paper, we study the geometry of the manifolds of geodesics of a Zoll surface of positive Gauss curvature, show how these metrics induce Finsler metrics of constant flag curvature and give some explicit constructions.

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.

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 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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