scholarly journals PROJECTIVELY RELATED EINSTEIN RANDERS SPACE.

2016 ◽  
Vol 4 (12) ◽  
pp. 777-785
Author(s):  
Narasimhamurthy S.K ◽  
◽  
Roopa M.K. ◽  
Keyword(s):  
Randers Space

On Flag Curvature of Homogeneous Randers Spaces

2013 ◽  
Vol 65 (1) ◽  
pp. 66-81 ◽  
Author(s):  
Shaoqiang Deng ◽  
Zhiguang Hu
Keyword(s):  
Explicit Formula ◽  
Lie Group ◽  
Flag Curvature ◽  
Nilpotent Lie Group ◽  
Finsler Spaces ◽  
Rigidity Result ◽  
Randers Space ◽  
Negatively Curved

AbstractIn this paper we give an explicit formula for the flag curvature of homogeneous Randers spaces of Douglas type and apply this formula to obtain some interesting results. We first deduce an explicit formula for the flag curvature of an arbitrary left invariant Randersmetric on a two-step nilpotent Lie group. Then we obtain a classification of negatively curved homogeneous Randers spaces of Douglas type. This results, in particular, in many examples of homogeneous non-Riemannian Finsler spaces with negative flag curvature. Finally, we prove a rigidity result that a homogeneous Randers space of Berwald type whose flag curvature is everywhere nonzero must be Riemannian.

Randers space forms

2004 ◽  
Vol 48 (1/2) ◽  
pp. 3-15 ◽  
Author(s):  
David Bao
Keyword(s):  
Space Forms ◽  
Randers Space

Classifications of Isoparametric Hypersurfaces in Randers Space Forms

2020 ◽  
Vol 36 (9) ◽  
pp. 1049-1060
Author(s):  
Qun He ◽  
Pei Long Dong ◽  
Song Ting Yin
Keyword(s):  
Space Forms ◽  
Isoparametric Hypersurfaces ◽  
Randers Space

Finsler Metrics with K = 0 and S = 0

2003 ◽  
Vol 55 (1) ◽  
pp. 112-132 ◽  
Author(s):  
Zhongmin Shen
Keyword(s):  
Euclidean Space ◽  
Shortest Path ◽  
External Force ◽  
Riemannian Space ◽  
Shortest Path Problem ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Randers Metric ◽  
Randers Space ◽  
Time Problem

AbstractIn the paper, we study the shortest time problem on a Riemannian space with an external force. We show that such problem can be converted to a shortest path problem on a Randers space. By choosing an appropriate external force on the Euclidean space, we obtain a non-trivial Randers metric of zero flag curvature. We also show that any positively complete Randers metric with zero flag curvature must be locally Minkowskian.

A Bernstein type theorem on a Randers space

2004 ◽  
Vol 329 (2) ◽  
pp. 291-305 ◽  
Author(s):  
Marcelo Souza ◽  
Joel Spruck ◽  
Keti Tenenblat
Keyword(s):  
Type Theorem ◽  
Bernstein Type ◽  
Randers Space ◽  
Bernstein Type Theorem

REVERSIBLE GEODESICS FOR (α, β)-METRICS

2010 ◽  
Vol 21 (08) ◽  
pp. 1071-1094 ◽  
Author(s):  
IOANA MONICA MASCA ◽  
VASILE SORIN SABAU ◽  
HIDEO SHIMADA
Keyword(s):  
Finsler Space ◽  
Finsler Metrics ◽  
Randers Space ◽  
Geodesic Paths

A Finsler space is said to have reversible geodesics if for any of its oriented geodesic paths, the same path traversed in the opposite sense is also a geodesic. In [6] the conditions for a Randers space to have reversible geodesics have been found. The main goal of this paper is to find conditions for a Finsler space endowed with an (α, β)-metric to be with reversible geodesics or strictly reversible geodesics, respectively. Moreover, we obtain some new classes of (α, β)-metrics with reversible geodesics and show how new Finsler metrics with reversible geodesics can be constructed by means of a Randers change.

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