A slice theorem for singular Riemannian foliations, with applications

Mendes, Ricardo; Radeschi, Marco

doi:10.1090/tran/7502

A slice theorem for singular Riemannian foliations, with applications
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by Ricardo A. E. Mendes and Marco Radeschi PDF

Trans. Amer. Math. Soc. 371 (2019), 4931-4949 Request permission

Abstract:

We prove a slice theorem around closed leaves in a singular Riemannian foliation, and we use it to study the $C^\infty$-algebra of smooth basic functions, generalizing to the inhomogeneous setting a number of results by G. Schwarz. In particular, in the infinitesimal case we show that this algebra is generated by a finite number of polynomials.

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