Advertisement

Results in Mathematics

, Volume 1, Issue 1–2, pp 156–194 | Cite as

Jacobi fields, totally geodesic foliations and geodesic differential forms

  • Peter Dombrowski
Forschungsbeiträge Research paper

Keywords

Vector Field Riemannian Manifold Vector Bundle Covariant Derivative Constant Curvature 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    K. Abe, A characterization of totally geodesic submanifolds in SN and CPsuN by an inequality, Tϕhoku Math. J. 23, 219–244 (1971).CrossRefGoogle Scholar
  2. [2]
    K. Abe, Applications of a Ricatti type differential equation to riemannian manifolds with totally geodesic distributions, Tøhoku Math. J. 25, 425–444 (1973).CrossRefMATHGoogle Scholar
  3. [3]
    J. F. Adams, Vectorfields on spheres, Ann. Math. 75, 603–632 (1962).CrossRefMATHGoogle Scholar
  4. [4]
    R. L. Bishop and B. O’Neill, Manifolds of negative curvature. Trans. Amer. Math. soc. 145, 1–49 (1969).MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    S. S. Chern and R. K. Lashof, On the total curvature of immersed manifolds, Amer. J. Math. 79, 306–318 (1957).MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    P. Dombrowski, On the geometry of the tangent bundle, J. reine angew. Math. 210, 73–88 (1962).MathSciNetMATHGoogle Scholar
  7. [7]
    P. Dombrowski, Maximale eindeutige Lösungen (Riemannsche Flächen) für Cauchysche Anfangswertaufgaben I, Math. Annalen 160, 195–232 (1965).MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    P. Dombrowski, Differentiale maps into riemannian manifolds of constant stable osculating rank I, J. reine angew. Math. 274/275, 310–341 (1975).MathSciNetMATHGoogle Scholar
  9. [9]
    D. Ferus, On the completeness of nullity foliations, Mich. Math. J. 18, 61–64 (1971).MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    D. Ferus, Totally geodesic foliations, Math. Ann. 188, 313–316 (1970).MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    A. Gray, Some relations between curvature and characteristic classes, Math. Annalen 184, 257–267 (1970).MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    P. Hartman and L. Nirenberg, On spherical image maps whose Jacobians do not change sign, Amer. J. Math. 81, 901–920 (1959).MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen I, 4-te Aufl., Leipzig, 1951.Google Scholar
  14. [14]
    S. Kobayashi and K. Nomizu, Foundation of Differential Geometry II, Interscience Publishers, New York, 1965.Google Scholar
  15. [15]
    R. Maltz, The nullity spaces of curvature- like tensors, J. Diff. Geometry 7, 519–523 (1972).MathSciNetMATHGoogle Scholar
  16. [16]
    B. O’Neill and E. Stiel, Isometric immersions of constant curvature manifolds, Mich. Math. J. 10, 335–339 (1963).MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    G. de Rham, On the area of complex manifolds, Seminar on several complex variables, Institute for Advanced Study, Princeton, 1957.Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 1978

Authors and Affiliations

  • Peter Dombrowski
    • 1
  1. 1.Mathematisches Institut der UniversitätKöln

Personalised recommendations