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Note on the residues of the singularities of a Riemannian foliation
Author:
Xiang Ming Mei
Journal:
Proc. Amer. Math. Soc. 89 (1983), 359-366
MSC:
Primary 53C12; Secondary 57R30
MathSciNet review:
712652
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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].
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Paul
Baum and Raoul
Bott, Singularities of holomorphic foliations, J. Differential
Geometry 7 (1972), 279–342. MR 0377923
(51 #14092)
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Paul
Baum, Structure of foliation singularities, Advances in Math.
15 (1975), 361–374. MR 0377125
(51 #13298)
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Connor
Lazarov and Joel
Pasternack, Residues and characteristic classes for Riemannian
foliations, J. Differential Geometry 11 (1976),
no. 4, 599–612. MR 0445514
(56 #3854)
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Seiki
Nishikawa, Residues and characteristic classes for projective
foliations, Japan. J. Math. (N.S.) 7 (1981),
no. 1, 45–108. MR 728329
(85b:57034)
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Kobayashi, Transformation groups in differential geometry,
Springer-Verlag, New York-Heidelberg, 1972. Ergebnisse der Mathematik und
ihrer Grenzgebiete, Band 70. MR 0355886
(50 #8360)
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Paul
Baum and Jeff
Cheeger, Infinitesimal isometries and Pontryagin numbers,
Topology 8 (1969), 173–193. MR 0238351
(38 #6627)
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J.
S. Pasternack, Foliations and compact Lie group actions,
Comment. Math. Helv. 46 (1971), 467–477. MR 0300307
(45 #9353)
- [1]
- P. Baum and R. Bott, Singularities of holomorphic foliations, J. Differential Geom. 7 (1972), 279-342. MR 0377923 (51:14092)
- [2]
- P. Baum, Structure of foliation singularities, Adv. in Math. 15 (1975), 361-374. MR 0377125 (51:13298)
- [3]
- C. Lazarov and J. Pasternack, Residues and characteristic classes for Riemannian foliations, J. Differential Geom. 11 (1976), 599-612. MR 0445514 (56:3854)
- [4]
- S. Nishikawa, Residues and characteristic classes for projective foliations, Japan. J. Math. 7 (1981), 45-108. MR 728329 (85b:57034)
- [5]
- S. Kobayashi, Transformation groups in differential geometry, Springer-Verlag, Berlin, 1972. MR 0355886 (50:8360)
- [6]
- P. Baum and J. Cheeger, Infinitesimal isometries and Pontrjagin numbers, Topology 8 (1969), 173-193. MR 0238351 (38:6627)
- [7]
- J. Pasternack, Foliation and compact Lie group action, Comment. Math. Helv 46 (1971), 467-477. MR 0300307 (45:9353)
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DOI:
http://dx.doi.org/10.1090/S0002-9939-1983-0712652-7
PII:
S 0002-9939(1983)0712652-7
Article copyright:
© Copyright 1983
American Mathematical Society
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