Parallel focal structure and singular Riemannian foliations

Töben, Dirk

doi:10.1090/S0002-9947-05-03829-8

Parallel focal structure and singular Riemannian foliations
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by Dirk Töben PDF

Trans. Amer. Math. Soc. 358 (2006), 1677-1704 Request permission

Abstract:

We give a necessary and sufficient condition for a submanifold with parallel focal structure to give rise to a global foliation of the ambient space by parallel and focal manifolds. We show that this is a singular Riemannian foliation with complete orthogonal transversals. For this object we construct an action on the transversals that generalizes the Weyl group action for polar actions.

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