Generalized Berwald Projective Weyl metrics

TL;DR

This paper introduces the generalized Berwald projective Weyl ($GB ilde{W}$) metric in Finsler geometry, demonstrating its invariance properties and its relation to generalized Douglas metrics and scalar curvature conditions.

Contribution

It defines a new $GB ilde{W}$ metric, proves its $C$-projective invariance, and explores its subset relations and curvature properties within Finsler geometry.

Findings

$GB ilde{W}$ metrics are $C$-projectively invariant.

All $GDW$ metrics with zero Landsberg curvature are R-quadratic.

$GDW$ metrics include all scalar curvature Finsler metrics.

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.