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 .
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 .
@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}, pages = {261--274}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {32}, number = {3}, year = {1982}, doi = {10.5802/aif.889}, mrnumber = {84c:57019}, zbl = {0466.57012}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.889/} }
TY - JOUR AU - Montesinos, Angel TI - Conformal curvature for the normal bundle of a conformal foliation JO - Annales de l'Institut Fourier PY - 1982 SP - 261 EP - 274 VL - 32 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.889/ DO - 10.5802/aif.889 LA - en ID - AIF_1982__32_3_261_0 ER -
%0 Journal Article %A Montesinos, Angel %T Conformal curvature for the normal bundle of a conformal foliation %J Annales de l'Institut Fourier %D 1982 %P 261-274 %V 32 %N 3 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.889/ %R 10.5802/aif.889 %G en %F AIF_1982__32_3_261_0
Montesinos, Angel. Conformal curvature for the normal bundle of a conformal foliation. Annales de l'Institut Fourier, Volume 32 (1982) no. 3, pp. 261-274. doi : 10.5802/aif.889. http://www.numdam.org/articles/10.5802/aif.889/
[1] Handbook of mathematical functions, Dover, New York, 1972. | Zbl
and , Ed.,[2] Some relations between curvature and characteristic classes, Math., Ann., 184 (1970), 257-267. | MR | Zbl
,[3] On the Bianchi identities, Math. Ann., 199 (1972), 175-204. | MR | Zbl
,[4] On certain classes of almost product structures, to appear. | Zbl
,[5] On characteristic classes of riemannian, conformal and projective foliations, J. Math. Soc. Japan, 28, 2 (1976), 223-241. | MR | Zbl
and ,[6] Foliations and compact Lie group actions, Com. Math. Helv., 46 (1971), 467-477. | MR | Zbl
,[7] On the area of complex manifolds, Seminar on Several Complex Variables, Institute for Advanced Study, 1957. | Zbl
,Cited by Sources: