On the Projective Algebra of Randers Metrics of Constant Flag Curvature

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 $\frac{n(n+1)}{2}$.

References in corpus (1)

• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry

Cited by in corpus (2)

• On the Dimension of the Group of Projective Transformations of Closed Randers and Riemannian Manifolds
• On projective symmetries on Finsler Spaces