# Conformal curvature for the normal bundle of a conformal foliation

Annales de l'institut Fourier (1982)

- Volume: 32, Issue: 3, page 261-274
- ISSN: 0373-0956

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topMontesinos, Angel. "Conformal curvature for the normal bundle of a conformal foliation." Annales de l'institut Fourier 32.3 (1982): 261-274. <http://eudml.org/doc/74551>.

@article{Montesinos1982,

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

author = {Montesinos, Angel},

journal = {Annales de l'institut Fourier},

keywords = {conformal curvature for the normal bundle of a conformal foliation; conformally flat; Pontrjagin classes},

language = {eng},

number = {3},

pages = {261-274},

publisher = {Association des Annales de l'Institut Fourier},

title = {Conformal curvature for the normal bundle of a conformal foliation},

url = {http://eudml.org/doc/74551},

volume = {32},

year = {1982},

}

TY - JOUR

AU - Montesinos, Angel

TI - Conformal curvature for the normal bundle of a conformal foliation

JO - Annales de l'institut Fourier

PY - 1982

PB - Association des Annales de l'Institut Fourier

VL - 32

IS - 3

SP - 261

EP - 274

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

LA - eng

KW - conformal curvature for the normal bundle of a conformal foliation; conformally flat; Pontrjagin classes

UR - http://eudml.org/doc/74551

ER -

## References

top- [1] M. ABRAMOWITZ and I.A. STEGUN, Ed., Handbook of mathematical functions, Dover, New York, 1972. Zbl0543.33001
- [2] A. GRAY, Some relations between curvature and characteristic classes, Math., Ann., 184 (1970), 257-267. Zbl0181.49901MR41 #6105
- [3] R.S. KULKARNI, On the Bianchi identities, Math. Ann., 199 (1972), 175-204. Zbl0234.53021MR49 #3767
- [4] A. MONTESINOS, On certain classes of almost product structures, to appear. Zbl0538.53044
- [5] S. NISHIKAWA and H. SATO, On characteristic classes of riemannian, conformal and projective foliations, J. Math. Soc. Japan, 28, 2 (1976), 223-241. Zbl0318.57025MR53 #4090
- [6] J. PASTERNACK, Foliations and compact Lie group actions, Com. Math. Helv., 46 (1971), 467-477. Zbl0228.57020MR45 #9353
- [7] G. DE RHAM, On the area of complex manifolds, Seminar on Several Complex Variables, Institute for Advanced Study, 1957. Zbl0192.44102

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