Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.08.08
  • Accepted : 2020.02.19
  • Published : 2020.07.01
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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.

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