Conformal curvature for the normal bundle of a conformal foliation

Angel Montesinos

Annales de l'institut Fourier (1982)

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

Abstract

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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 .

How to cite

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Montesinos, 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

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  1. [1] M. ABRAMOWITZ and I.A. STEGUN, Ed., Handbook of mathematical functions, Dover, New York, 1972. Zbl0543.33001
  2. [2] A. GRAY, Some relations between curvature and characteristic classes, Math., Ann., 184 (1970), 257-267. Zbl0181.49901MR41 #6105
  3. [3] R.S. KULKARNI, On the Bianchi identities, Math. Ann., 199 (1972), 175-204. Zbl0234.53021MR49 #3767
  4. [4] A. MONTESINOS, On certain classes of almost product structures, to appear. Zbl0538.53044
  5. [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. [6] J. PASTERNACK, Foliations and compact Lie group actions, Com. Math. Helv., 46 (1971), 467-477. Zbl0228.57020MR45 #9353
  7. [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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