This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental...This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10871149)Doctoral Fund of Education of China (Grant No. 200804860046)
文摘This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.
