Abstract
This paper introduces a new quantity in Finsler geometry, called the generalized Berwald projective Weyl (\(GB\widetilde{W}\)) metric. The C-projective invariance of these metrics is demonstrated, and it is shown that they constitute a proper subset of the class of generalized Douglas (GDW) metrics. The paper also proves that all GDW metrics with vanishing Landsberg curvature are of R-quadratic type. The class of GDW metrics contains all Finsler metrics of scalar curvature, which provides an extension of the well-known Numata’s theorem.
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Significance Statement This paper introduces a novel C-projective invariant quantity, called \(GB\widetilde{W}\) (Generalized Berwald projective Weyl), in Finsler geometry. The definition of this quantity was inspired by the well-known quantity GDW (Generalized Douglas Weyl), and it encompasses all Finsler metrics with a constant flag curvature (\(n>2\)). Additionally, the paper proves an extension of Numata’s theorem, a famous theorem in Finsler geometry.
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Sadeghzadeh, N. Generalized Berwald Projective Weyl (\(GB\widetilde{W}\)) Metrics. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 94, 487–492 (2024). https://doi.org/10.1007/s40010-024-00896-6
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DOI: https://doi.org/10.1007/s40010-024-00896-6