On a conjecture of Stolz in the toric case

Abstract

In 1996 Stolz [Math. Ann. 304 (1996), pp. 785–800] conjectured that a string manifold with positive Ricci curvature has vanishing Witten genus. Here we prove this conjecture for toric string Fano manifolds and for string torus manifolds admitting invariant metrics of non-negative sectional curvature.