Skip to main content
Log in

Jacobi fields, totally geodesic foliations and geodesic differential forms

  • Forschungsbeiträge Research paper
  • Published:
Results in Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. K. Abe, A characterization of totally geodesic submanifolds in SN and CPsuN by an inequality, Tϕhoku Math. J. 23, 219–244 (1971).

    Article  Google Scholar 

  2. K. Abe, Applications of a Ricatti type differential equation to riemannian manifolds with totally geodesic distributions, Tøhoku Math. J. 25, 425–444 (1973).

    Article  MATH  Google Scholar 

  3. J. F. Adams, Vectorfields on spheres, Ann. Math. 75, 603–632 (1962).

    Article  MATH  Google Scholar 

  4. R. L. Bishop and B. O’Neill, Manifolds of negative curvature. Trans. Amer. Math. soc. 145, 1–49 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  5. S. S. Chern and R. K. Lashof, On the total curvature of immersed manifolds, Amer. J. Math. 79, 306–318 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  6. P. Dombrowski, On the geometry of the tangent bundle, J. reine angew. Math. 210, 73–88 (1962).

    MathSciNet  MATH  Google Scholar 

  7. P. Dombrowski, Maximale eindeutige Lösungen (Riemannsche Flächen) für Cauchysche Anfangswertaufgaben I, Math. Annalen 160, 195–232 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  8. P. Dombrowski, Differentiale maps into riemannian manifolds of constant stable osculating rank I, J. reine angew. Math. 274/275, 310–341 (1975).

    MathSciNet  MATH  Google Scholar 

  9. D. Ferus, On the completeness of nullity foliations, Mich. Math. J. 18, 61–64 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  10. D. Ferus, Totally geodesic foliations, Math. Ann. 188, 313–316 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Gray, Some relations between curvature and characteristic classes, Math. Annalen 184, 257–267 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Hartman and L. Nirenberg, On spherical image maps whose Jacobians do not change sign, Amer. J. Math. 81, 901–920 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  13. E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen I, 4-te Aufl., Leipzig, 1951.

  14. S. Kobayashi and K. Nomizu, Foundation of Differential Geometry II, Interscience Publishers, New York, 1965.

  15. R. Maltz, The nullity spaces of curvature- like tensors, J. Diff. Geometry 7, 519–523 (1972).

    MathSciNet  MATH  Google Scholar 

  16. B. O’Neill and E. Stiel, Isometric immersions of constant curvature manifolds, Mich. Math. J. 10, 335–339 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  17. G. de Rham, On the area of complex manifolds, Seminar on several complex variables, Institute for Advanced Study, Princeton, 1957.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dombrowski, P. Jacobi fields, totally geodesic foliations and geodesic differential forms. Results. Math. 1, 156–194 (1978). https://doi.org/10.1007/BF03322935

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322935

Keywords

Navigation