English

Euclidean hypersurfaces with a totally geodesic foliation of codimension one

Differential Geometry 2014-01-27 v2

Abstract

We classify the hypersurfaces of Euclidean space that carry a totally geodesic foliation with complete leaves of codimension one. In particular, we show that rotation hypersurfaces with complete profiles of codimension one are characterized by their warped product structure. The local version of the problem is also considered.

Keywords

Cite

@article{arxiv.1306.4570,
  title  = {Euclidean hypersurfaces with a totally geodesic foliation of codimension one},
  author = {M. Dajczer and V. Rovenski and R. Tojeiro},
  journal= {arXiv preprint arXiv:1306.4570},
  year   = {2014}
}

Comments

15 pages. Final version. To appear in Geometriae Dedicatta. Theorem 6 in the previous version removed, details on some of the proofs added, overall exposition improved