Article

Geometriae Dedicata

, Volume 108, Issue 1, pp 141-152

First online:

Integrable Riemannian Submersion with Singularities

  • Marcos M. AlexandrinoAffiliated withDept de Matemática, Pontifícia Universidade Católica do Rio de Janeiro

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Abstract

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 foliations isoparametric maps Riemannian submersions equifocal submanifolds