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May 9, 2026Mathematics Open0 citationsOpen Access

Projective vector fields on Exponential (α, β)-metrics

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SSSeyedeh Yasaman SadatiUniversity of MazandaranMRMehdi Rafie-RadUniversity of Mazandaran

Key Points

  • The research aims to explore the characteristics of projective vector fields in a specific class of (α, β)-metrics.
  • Analyzed projective algebra associated with (α, β)-metrics
  • Investigated conditions under which exponential (α, β)-metrics admit projective vector fields
  • Utilized Lie algebra concepts to assess vector field properties.
  • Demonstrated that projective vector fields in the studied metrics are conformal with respect to the Riemannian metric α.
  • Found that if a certain condition is met, the S-curvature vanishes, implying significant geometric implications.

Abstract

This paper is devoted to the study of the projective algebra of a certain class of (α, β)- metrics. The projective algebra of a Finsler space is a finite-dimensional Lie algebra with respect to the usual Lie bracket. We show that if an exponential (α, β)-metric F = αexp(s), s = β/α, admits a projective vector field, then V is a conformal vector field with respect to the Riemannian metric α or F has vanishing S-curvature.

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Cite This Study

Sadati et al. (2026) studied this question.

synapsesocial.com/papers/69fed16ab9154b0b82878bd4https://doi.org/10.1142/s2811007226500100
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