On projective equivalence and pointwise projective relation of Randers metrics

TL;DR

This paper corrects a previous error and extends the projective Lichnerowicz-Obata conjecture to Randers metrics, advancing the understanding of their geometric properties.

Contribution

It provides a correction to prior work and generalizes a fundamental conjecture in Finsler geometry specifically for Randers metrics.

Findings

Corrects a mistake in previous literature

Proves a generalized version of the projective Lichnerowicz-Obata conjecture for Randers metrics

Enhances understanding of projective relations in Finsler geometry

Abstract

We correct a mistake in Shen Yibing, Yu Yaoyong, On Projectively Related Randers Metrics, International Journal of Mathematics 19}(2008), no. 5, 503--520, and prove the natural generalization of the projective Lichnerowicz-Obata conjecture for Randers metrics.