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This article is cited in 10 scientific papers (total in 10 papers)
On the Projective Algebra of Randers Metrics of Constant Flag Curvature
Mehdi Rafie-Radab, Bahman Rezaeic a Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1467, Babolsar, Iran
b School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
c Department of Mathematics, Faculty of Sciences, University of Urmia, Urmia, Iran
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 $p(M,F=\alpha+\beta)$ of a Randers space is characterized as a certain Lie subalgebra of the projective algebra $p(M,\alpha)$. 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 $\frac{n(n+1)}{2}$.
Keywords:
Randers metric; constant flag curvature; projective vector field; projective algebra.
Received: February 26, 2011; in final form August 20, 2011; Published online August 31, 2011
Citation:
Mehdi Rafie-Rad, Bahman Rezaei, “On the Projective Algebra of Randers Metrics of Constant Flag Curvature”, SIGMA, 7 (2011), 085, 12 pp.
Linking options:
https://www.mathnet.ru/eng/sigma643 https://www.mathnet.ru/eng/sigma/v7/p85
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