Note on the residues of the singularities of a Riemannian foliation

Mei, Xiang Ming

doi:10.1090/S0002-9939-1983-0712652-7

Note on the residues of the singularities of a Riemannian foliation
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by Xiang Ming Mei PDF

Proc. Amer. Math. Soc. 89 (1983), 359-366 Request permission

Abstract:

We generalize the result of Lazarov and Pasternack [3] on the residues of the singularities of a Riemannian foliation and give an explicit formula of the residues of the connected components of the singular set of a Riemannian foliation without any restriction on the dimension of the connected components of its singular set. This formula is also the generalization of the residues formula of the zero set of the Killing vector field due to Baum and Cheeger [6].

References

Paul Baum and Raoul Bott, Singularities of holomorphic foliations, J. Differential Geometry 7 (1972), 279–342. MR 377923
Paul Baum, Structure of foliation singularities, Advances in Math. 15 (1975), 361–374. MR 377125, DOI 10.1016/0001-8708(75)90142-5
Connor Lazarov and Joel Pasternack, Residues and characteristic classes for Riemannian foliations, J. Differential Geometry 11 (1976), no. 4, 599–612. MR 445514
Seiki Nishikawa, Residues and characteristic classes for projective foliations, Japan. J. Math. (N.S.) 7 (1981), no. 1, 45–108. MR 728329, DOI 10.4099/math1924.7.45
Shoshichi Kobayashi, Transformation groups in differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70, Springer-Verlag, New York-Heidelberg, 1972. MR 0355886
Paul Baum and Jeff Cheeger, Infinitesimal isometries and Pontryagin numbers, Topology 8 (1969), 173–193. MR 238351, DOI 10.1016/0040-9383(69)90008-1
J. S. Pasternack, Foliations and compact Lie group actions, Comment. Math. Helv. 46 (1971), 467–477. MR 300307, DOI 10.1007/BF02566859