Conformal curvature for the normal bundle of a conformal foliation
Montesinos, Angel
Annales de l'Institut Fourier, Tome 32 (1982), p. 261-274 / Harvested from Numdam

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

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

@article{AIF_1982__32_3_261_0,
     author = {Montesinos, Angel},
     title = {Conformal curvature for the normal bundle of a conformal foliation},
     journal = {Annales de l'Institut Fourier},
     volume = {32},
     year = {1982},
     pages = {261-274},
     doi = {10.5802/aif.889},
     mrnumber = {84c:57019},
     zbl = {0466.57012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1982__32_3_261_0}
}
Montesinos, Angel. Conformal curvature for the normal bundle of a conformal foliation. Annales de l'Institut Fourier, Tome 32 (1982) pp. 261-274. doi : 10.5802/aif.889. http://gdmltest.u-ga.fr/item/AIF_1982__32_3_261_0/

[1] M. Abramowitz and I.A. Stegun, Ed., Handbook of mathematical functions, Dover, New York, 1972. | Zbl 0543.33001

[2] A. Gray, Some relations between curvature and characteristic classes, Math., Ann., 184 (1970), 257-267. | MR 41 #6105 | Zbl 0181.49901

[3] R.S. Kulkarni, On the Bianchi identities, Math. Ann., 199 (1972), 175-204. | MR 49 #3767 | Zbl 0234.53021

[4] A. Montesinos, On certain classes of almost product structures, to appear. | Zbl 0538.53044

[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 53 #4090 | Zbl 0318.57025

[6] J. Pasternack, Foliations and compact Lie group actions, Com. Math. Helv., 46 (1971), 467-477. | MR 45 #9353 | Zbl 0228.57020

[7] G. De Rham, On the area of complex manifolds, Seminar on Several Complex Variables, Institute for Advanced Study, 1957. | Zbl 0192.44102