Isometric immersions into warped product spaces

Abstract

This paper concerns the submanifold geometry in the ambient space of warped product manifolds Fn ×σ ℝ, this is a large family of manifolds including the usual space forms ℝm, \( \mathbb{S}^m \) and ℝm. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space ℝn ×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.