Geometriae Dedicata

, Volume 108, Issue 1, pp 141–152

Integrable Riemannian Submersion with Singularities

  • Marcos M. Alexandrino

DOI: 10.1007/s10711-004-1776-5

Cite this article as:
Alexandrino, M.M. Geometriae Dedicata (2004) 108: 141. doi:10.1007/s10711-004-1776-5


A map of a Riemannian manifold into an euclidian space is said to be transnormal if its restrictions to neighbourhoods of regular level sets are integrable Riemannian submersions. Analytic transnormal maps can be used to describe isoparametric submanifolds in spaces of constant curvature and equifocal submanifolds with flat sections in simply connected symmetric spaces. These submanifolds are also regular leaves of singular Riemannian foliations with sections. We prove that regular level sets of an analytic transnormal map on a real analytic complete Riemannian manifold are equifocal submanifolds and leaves of a singular Riemannian foliation with sections.

singular Riemannian foliationsisoparametric mapsRiemannian submersionsequifocal submanifolds

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Marcos M. Alexandrino
    • 1
  1. 1.Dept de MatemáticaPontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil