New classes of projectively related Finsler metrics of constant flag curvature

We define a Weyl-type curvature tensor of [Formula: see text]-type to provide a characterization for Finsler metrics of constant flag curvature. This Weyl-type curvature tensor is projective invariant only to projective factors that are Hamel functions. Based on this aspect, we construct new families of projectively related Finsler metrics that have constant flag curvature.

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On a class of two-dimensional projectively flat finsler metrics with constant flag curvature

Acta Mathematica Sinica English Series ◽

10.1007/s10114-013-0728-0 ◽

2013 ◽

Vol 29 (5) ◽

pp. 959-974 ◽

Cited By ~ 2

Author(s):

Guo Jun Yang

Keyword(s):

Flag Curvature ◽

Finsler Metrics ◽

Two Dimensional ◽

Constant Flag Curvature ◽

Projectively Flat

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The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature

Symmetry Integrability and Geometry Methods and Applications ◽

10.3842/sigma.2009.045 ◽

2009 ◽

Cited By ~ 1

Author(s):

Enli Guo

Keyword(s):

Explicit Construction ◽

Flag Curvature ◽

Finsler Metrics ◽

Constant Flag Curvature

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

Differential Geometry and its Applications ◽

10.1016/j.difgeo.2019.101579 ◽

2020 ◽

Vol 68 ◽

pp. 101579

Author(s):

Guocai Cai ◽

Chunhui Qiu ◽

Xiuling Wang

Keyword(s):

Flag Curvature ◽

Finsler Metrics ◽

Constant Flag Curvature ◽

Projectively Flat

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On a Class of Projectively Flat Metrics with Constant Flag Curvature

Canadian Journal of Mathematics ◽

10.4153/cjm-2008-021-1 ◽

2008 ◽

Vol 60 (2) ◽

pp. 443-456 ◽

Cited By ~ 28

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.

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

International Journal of Mathematics ◽

10.1142/s0129167x07004291 ◽

2007 ◽

Vol 18 (07) ◽

pp. 749-760 ◽

Cited By ~ 27

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.

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