We prove the existence of at least two distinct closed geodesics on a compact simply connected manifold M with a bumpy and irreversible Finsler metric, when H* (M; Q) congruent to T-d,T-h+1(x) for some integer h >= 2 and even integer d >= 2. Consequently, together with earlier results on S-n, it implies the existence of at least two distinct closed geodesics on every compact simply connected manifold M with a bumpy irreversible Finsler metric.
展开▼
