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Lie groupoids and semi-local models of singular Riemannian foliations

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Abstract

We describe a local model for any singular Riemannian foliation in a neighborhood of a closed saturated submanifold of a singular stratum. Moreover, we construct a Lie groupoid that controls the transverse geometry of the linear approximation of the singular Riemannian foliation around these submanifolds. We also discuss the closure of this Lie groupoid and its Lie algebroid.

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Acknowledgements

The authors thank Fernando M. Escobosa, Ivo Terek and Leonardo F. Cavenaghi for their useful suggestions and to the anonymous referee for valuable comments.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508 090, São Paulo, Brazil

    Marcos M. Alexandrino, Marcelo K. Inagaki, Mateus de Melo & Ivan Struchiner

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  1. Marcos M. Alexandrino
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  2. Marcelo K. Inagaki
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  3. Mateus de Melo
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  4. Ivan Struchiner
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The first author was supported by grand \(\#\) 2016/23746-6, São Paulo Research Foundation (FAPESP). The second author was supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico). The third author was supported by grant \(\#\) 2019/14777-3, São Paulo Research Foundation (FAPESP). The fourth author was supported by grant \(\#\) 2015/22059-2, São Paulo Research Foundation (FAPESP) and CNPq (307131/2016-5). In addition, this study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Brasil (CAPES)-Finance Code 001.

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Alexandrino, M.M., Inagaki, M.K., de Melo, M. et al. Lie groupoids and semi-local models of singular Riemannian foliations. Ann Glob Anal Geom 61, 593–619 (2022). https://doi.org/10.1007/s10455-021-09813-1

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  • DOI: https://doi.org/10.1007/s10455-021-09813-1

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