On prouve que le fibré normal d’une distribution dans une variété riemannienne admet une courbure conforme si et seulement si est un feuilletage conforme. Alors, est conformément plat si et seulement si est nulle. De plus, on peut exprimer les classes de Pontrjagin de en fonction de .
It is proved that the normal bundle of a distribution on a riemannian manifold admits a conformal curvature if and only if is a conformal foliation. Then is conformally flat if and only if vanishes. Also, the Pontrjagin classes of can be expressed in terms of .
@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/
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