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On Finsler Surfaces with Isotropic Main Scalar

Author

Listed:
  • Akbar Tayebi

    (Department of Mathematics, Faculty of Science, University of Qom, Qom 3716146611, Iran)

  • Wei Sin Koh

    (Faculty of Business and Communications, INTI International University, Putra Nilai, Nilai 71800, Negeri Sembilan, Malaysia)

Abstract

Let ( M , F ) be a Finsler surface with the isotropic main scalar I = I ( x ) . The well-known Berwald’s theorem states that F is a Berwald metric if and only if it has a constant main scalar I = c o n s t a n t . This ensures a kind of equality of two non-Riemannian quantities for Finsler surfaces. In this paper, we consider a positively curved Finsler surface and show that H = 0 if and only if I = 0 . This provides an extension of Berwald’s theorem. It follows that F has an isotropic scalar flag curvature if and only if it is Riemannian. Our results yield an infrastructural development of some equalities for two-dimensional Finsler manifolds.

Suggested Citation

  • Akbar Tayebi & Wei Sin Koh, 2024. "On Finsler Surfaces with Isotropic Main Scalar," Mathematics, MDPI, vol. 12(13), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2141-:d:1430891
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