On Finsler Surfaces with Isotropic Main Scalar

Akbar Tayebi () and Wei Sin Koh
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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

Mathematics, 2024, vol. 12, issue 13, 1-10

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.

Keywords: Finsler surface; main scalar; flag curvature; H-curvature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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