Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 085, 12 pages      arXiv:1108.6127      https://doi.org/10.3842/SIGMA.2011.085

On the Projective Algebra of Randers Metrics of Constant Flag Curvature

Mehdi Rafie-Rad a, b and Bahman Rezaei c
a) School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
b) Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1467, Babolsar, Iran
c) Department of Mathematics, Faculty of Sciences, University of Urmia, Urmia, Iran

Received February 26, 2011, in final form August 20, 2011; Published online August 31, 2011

Abstract
The collection of all projective vector fields on a Finsler space (M,F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra denoted by p(M,F) and is the Lie algebra of the projective group P(M,F). The projective algebra p(M,F=α+β) of a Randers space is characterized as a certain Lie subalgebra of the projective algebra p(M,α). Certain subgroups of the projective group P(M,F) and their invariants are studied. The projective algebra of Randers metrics of constant flag curvature is studied and it is proved that the dimension of the projective algebra of Randers metrics constant flag curvature on a compact n-manifold either equals n(n+2) or at most is n(n+1)/2.

Key words: Randers metric; constant flag curvature; projective vector field; projective algebra.

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