Synge type theorems for positively curved Finsler manifolds (Q928481)

The author follows the ideology of \textit{L. Kozma} and \textit{I. R. Peter} [J. Math. Kyoto Univ. 46, No. 2, 377--382 (2006; Zbl 1178.53077)] to obtain a result similar to Weinstein's theorem in the case of a Finsler manifold \(M^n\) with \(k\)-th Ricci curvature bounded from below by \(\text{Ric}_k \geq k\). Let \(f\) be an isometry of \(M^n\) satisfying \(\text{dist}(x, f(x)) > \pi\sqrt{(k-1)/k}\) for all \(x \in M^n\). Then \(f\) reverses (respectively, preserves) orientation if \(n\) is even (respectively odd). Two Synge type theorems related to torus actions on Finsler manifold of positive flag curvature follow as corollaries.