no. 3
Conformal curvature for the normal bundle of a conformal foliation
Annales de l'Institut Fourier, Tome 32 (1982) no. 3, pp. 261-274.

On prouve que le fibré normal ℋ d’une distribution 𝒱 dans une variété riemannienne admet une courbure conforme C si et seulement si 𝒱 est un feuilletage conforme. Alors, ℋ est conformément plat si et seulement si C est nulle. De plus, on peut exprimer les classes de Pontrjagin de ℋ en fonction de C.

It is proved that the normal bundle ℋ of a distribution 𝒱 on a riemannian manifold admits a conformal curvature C if and only if 𝒱 is a conformal foliation. Then ℋ is conformally flat if and only if C vanishes. Also, the Pontrjagin classes of ℋ can be expressed in terms of C.

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     author = {Montesinos, Angel},
     title = {Conformal curvature for the normal bundle of a conformal foliation},
     journal = {Annales de l'Institut Fourier},
     pages = {261--274},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {32},
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     year = {1982},
     doi = {10.5802/aif.889},
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Montesinos, Angel. Conformal curvature for the normal bundle of a conformal foliation. Annales de l'Institut Fourier, Tome 32 (1982) no. 3, pp. 261-274. doi : 10.5802/aif.889. http://archive.numdam.org/articles/10.5802/aif.889/

[1] M. Abramowitz and I.A. Stegun, Ed., Handbook of mathematical functions, Dover, New York, 1972. | Zbl

[2] A. Gray, Some relations between curvature and characteristic classes, Math., Ann., 184 (1970), 257-267. | MR | Zbl

[3] R.S. Kulkarni, On the Bianchi identities, Math. Ann., 199 (1972), 175-204. | MR | Zbl

[4] A. Montesinos, On certain classes of almost product structures, to appear. | Zbl

[5] S. Nishikawa and H. Sato, On characteristic classes of riemannian, conformal and projective foliations, J. Math. Soc. Japan, 28, 2 (1976), 223-241. | MR | Zbl

[6] J. Pasternack, Foliations and compact Lie group actions, Com. Math. Helv., 46 (1971), 467-477. | MR | Zbl

[7] G. De Rham, On the area of complex manifolds, Seminar on Several Complex Variables, Institute for Advanced Study, 1957. | Zbl

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