Annals of Global Analysis and Geometry

, Volume 55, Issue 2, pp 309–323 | Cite as

Singular Riemannian flows and characteristic numbers

  • Igor Prokhorenkov
  • Ken RichardsonEmail author


Let M be an even-dimensional, oriented closed manifold. We show that the restriction of a singular Riemannian flow on M to a small tubular neighborhood of each connected component of its singular stratum is foliated diffeomorphic to an isometric flow on the same neighborhood. We then prove a formula that computes characteristic numbers of M as the sum of residues associated with the infinitesimal foliation at the components of the singular stratum of the flow.


Singular Riemannian foliation Characteristic numbers Transverse Killing vector field 

Mathematics Subject Classification

57R20 53C12 57R30 


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsTexas Christian UniversityFort WorthUSA

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