Isometric immersions into warped product spaces (Q627557)

The authors study isometric immersions of hypersurfaces into a warped product space, where one of the factors is one dimensional and the other factor is \(\mathbb R^n\). The study of submanifolds of such spaces was initiated in a series of papers by L. J. Alias and M. Dajczer around 2007. The main result of the present paper proves an existence result for such an immersion, provided suitable integrability conditions of Gauss, Codazzi and Ricci type are satisfied.