Skip to main content

Harmonic foliations

Part of the Lecture Notes in Mathematics book series (LNM,volume 949)

Keywords

  • Fundamental Form
  • Normal Bundle
  • Riemannian Submersion
  • Riemannian Foliation
  • Minimal Submanifolds

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10(1978), 1–68.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86(1964), 109–160.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. D. B. A. Epstein, Foliations with all leaves compact, Ann. Inst. Fourier 26(1976), 265–282.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. D. B. A. Epstein, Foliations with all leaves compact, Lecture Notes in Mathematics 468(1974), 1–2.

    CrossRef  Google Scholar 

  5. D. B. A. Epstein and H. Rosenberg, Stability of compact foliations, Lecture Notes in Mathematics 652(1978), 151–160.

    MathSciNet  Google Scholar 

  6. C. Godbillon et J. Vey, Un invariant des feuilletages de codimension un, C. R. Acad. Sc. Paris 273(1971), 92–95.

    MathSciNet  MATH  Google Scholar 

  7. A. Haefliger, Some remarks on foliations with minimal leaves, to appear.

    Google Scholar 

  8. H. L. Heitsch, Independent variation of secondary classes, Annals of Math. 108(1978), 421–460.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. R. S. Hamilton, Deformation theory of foliations, preprint Cornell University (1978).

    Google Scholar 

  10. S. Kobayashi and K. Nomizu, Foundations of differential geometry I, II (1963, 1969).

    Google Scholar 

  11. F. W. Kamber and Ph. Tondeur, Invariant differential operators and the cohomology of Lie algebra sheaves, Memoirs Amer. Math. Soc. 113(1971), 1–125.

    MathSciNet  MATH  Google Scholar 

  12. F. W. Kamber and Ph. Tondeur, Characteristic invariants of foliated bundles, Manuscripta Math. 11(1974), 51–89.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. F. W. Kamber and Ph. Tondeur, Foliated bundles and characteristic classes, Lecture Notes in Mathematics 493 (1975).

    Google Scholar 

  14. F. W. Kamber and Ph. Tondeur, Non-trivial characteristic invariants of homogeneous foliated bundles, Ann. Scient. Ec. Norm. Sup. 8(1975), 433–486.

    MathSciNet  MATH  Google Scholar 

  15. F. W. Kamber and Ph. Tondeur, On the linear independence of certain cohomology classes of BΓ, Advances in Math. Suppl. Studies 5(1979), 213–263.

    MathSciNet  Google Scholar 

  16. F. W. Kamber and Ph. Tondeur, Feuilletages harmoniques, C. R. Acad. Sc. Paris 291(1980), 409–411.

    MathSciNet  MATH  Google Scholar 

  17. F. W. Kamber and Ph. Tondeur, Infinitesimal automorphisms and second variation of the energy for harmonic foliations, to appear.

    Google Scholar 

  18. H. B. Lawson, Jr., Lectures on minimal submanifolds, Vol. I (1980), Publish or Perish, Inc.

    Google Scholar 

  19. C. Lazarov and J. Pasternak, Residues and characteristic classes for Riemannian foliations, J. Diff. Geom. 11(1976), 599–612.

    MathSciNet  MATH  Google Scholar 

  20. B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13(1966), 459–469.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. J. Pasternack, Foliations and compact Lie group actions, Comment. Math. Helv. 46(1971), 467–477.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. B. L. Reinhart, Foliated manifolds with bundle-like metrics, Annals. of Math. 69(1959), 119–132.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. B. L. Reinhart, The second fundamental form of a plane field, J. Differential Geometry 12(1977), 619–627.

    MathSciNet  MATH  Google Scholar 

  24. H. Rummler, Quelques notions simples en géométrie riemannienne et leurs applications aux feuilletages compacts, Comment. Math. Helv. 54(1979), 224–239.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. H. Rummler, Kompakte Blätterungen durch Minimalflächen, Habilitationsschrift Universität Freiburg i. Ue. (1979).

    Google Scholar 

  26. E. Ruh and J. Vilms, The tension field of the Gauss map, Transactions Amer. Math. Soc. 149(1970), 569–573.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. D. Sullivan, A homological characterization of foliations consisting of minimal surfaces, Comment. Math. Helv. 54(1979), 218–223.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Kamber, F.W., Tondeur, P. (1982). Harmonic foliations. In: Knill, R.J., Kalka, M., Sealey, H.C.J. (eds) Harmonic Maps. Lecture Notes in Mathematics, vol 949. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069758

Download citation

  • DOI: https://doi.org/10.1007/BFb0069758

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11595-3

  • Online ISBN: 978-3-540-39360-3

  • eBook Packages: Springer Book Archive