Bulletin of the
Korean Mathematical Society BKMS

We establish the generalized Myers theorem for Finsler manifolds under integral Ricci curvature bound. More precisely, we show that the forward complete Finsler $n$-manifold whose part of Ricci curvature less than a positive constant is small in $L^p$-norm (for $p>n/2$) have bounded diameter and finite fundamental group.

Keywords: extreme volume form, Finsler manifold, Ricci curvature, uniformity constant, fundamental group

MSC numbers: Primary 53C60; Secondary 53B40