Multiple closed geodesics on Riemannian 3-spheres (Q2641919)

The authors prove that on every compact simply connected Riemannian \textbf{Q}-homological 3-sphere \((M,g)\) with injectivity radius \(\text{inj}(M)\geq\pi\) and the sectional curvature \(K\) satisfying \({1 \over 16}<K\leq 1\), there exist at least two geometrically distinct closed geodesics.