Isometric immersions into warped product spaces

Qun Chen; Cai Rong Xiang
December 2010
Acta Mathematica Sinica;Dec2010, Vol. 26 Issue 12, p2269
Academic Journal
This paper concerns the submanifold geometry in the ambient space of warped product manifolds F × ℝ, this is a large family of manifolds including the usual space forms ℝ, $$ \mathbb{S}^m $$ and ℝ. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space ℝ × 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.


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