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SPECIAL PROJECTIVE ALGEBRA OF RANDERS METRICS OF CONSTANT S-CURVATURE

M. RAFIE-RAD

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

https://doi.org/10.1142/S021988781250034XCited by:2 (Source: Crossref)

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. A specific Lie sub-algebra of projective algebra of Randers spaces (called the special projective algebra) of non-zero constant S-curvature is studied and it is proved that its dimension is at most . Moreover, a local characterization of Randers spaces whose special projective algebra has maximum dimension is established. The results uncover somehow the complexity of projective Finsler geometry versus Riemannian geometry.

Keywords:

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