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http://dx.doi.org/10.4134/JKMS.j190552

ON THE C-PROJECTIVE VECTOR FIELDS ON RANDERS SPACES  

Rafie-Rad, Mehdi (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Shirafkan, Azadeh (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 1005-1018 More about this Journal
Abstract
A characterization of the C-projective vector fields on a Randers space is presented in terms of 𝚵-curvature. It is proved that the 𝚵-curvature is invariant for C-projective vector fields. The dimension of the algebra of the C-projective vector fields on an n-dimensional Randers space is at most n(n + 2). The generalized Funk metrics on the n-dimensional Euclidean unit ball 𝔹n(1) are shown to be explicit examples of the Randers metrics with a C-projective algebra of maximum dimension n(n+2). Then, it is also proved that an n-dimensional Randers space has a C-projective algebra of maximum dimension n(n + 2) if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.
Keywords
Randers metric; projective vector field; S-curvature; ${\Xi}$-curvature;
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Times Cited By KSCI : 2  (Citation Analysis)
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