纤维丛的全测地子流形

Totally geodesic submanifolds in a fibre bundle

本文证明了底空间Ｍ是纤维丛Ｐ的全测地子流形；并且在ｄｉｍＰ－ｄｉｍＭ＝２时证明了若Ｐ是平坦的，则Ｐ的每一纤维也是全测地子流形．

In the paper,we prove that if P is a fiber bundle of a Riemannian Manifold M,then M is a totally geodesic submanifold of P. Moreover when dimP-dimM=2 and P is flat,then we prove that every fiber of P is a totally geodesic submanifold of P.