Tohoku Mathematical Journal

Totally geodesic foliations and Killing fields

Gen-ichi Oshikiri

Full-text: Open access

Article information

Source
Tohoku Math. J. (2) Volume 35, Number 3 (1983), 387-392.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
http://projecteuclid.org/euclid.tmj/1178228997

Digital Object Identifier
doi:10.2748/tmj/1178228997

Mathematical Reviews number (MathSciNet)
MR0711354

Zentralblatt MATH identifier
0517.53035

Subjects
Primary: 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32]
Secondary: 57R30: Foliations; geometric theory

Citation

Oshikiri, Gen-ichi. Totally geodesic foliations and Killing fields. Tohoku Math. J. (2) 35 (1983), no. 3, 387--392. doi:10.2748/tmj/1178228997. http://projecteuclid.org/euclid.tmj/1178228997.


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References

  • [1] R. L. BISHOP AND B. O'NEIL, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
  • [2] H. IMANISHI, On the theorem of Denjoy-Sacksteder for codimention-onefoliations withou holonomy, 3. Math. Kyoto Univ., 14 (1974), 607-634.
  • [3] D. L. JOHNSON AND L. B. WHITT, Totally geodesic foliations, 3. Differential Geom., 1 (1980), 225-235.
  • [4] S. KASHIWABARA, The decomposition of a differentiate manifold and its applications, Thoku Math. 3., 11 (1959), 43-53.
  • [5] G. OSHIKIRI, Jacobi fields and the stability of leaves of codimension-one minimal folia tions, Thoku Math. J., 34 (1982), 417-424.
  • [6] G. REEB, Sur certaines proprietes topologiques des varietes feuilletees, Actualites Sci Ind., no. 1183, Publ. Inst. Math. Univ. Strasbourg, 11, 91-154, 157-158. Hermann, Paris, 1952.
  • [7] H. RUMMLER, Quelques notions simples en geometrie riemannienne et leurs application aux feuilletages, Commemt. Math. Helv., 54 (1979), 224-239.
  • [8] F. W. KAMBER AND P. TONDEUR, Harmonic foliations, Proc. NSF Conference on Harmoni Maps, Tulane Univ., 1980, Lecture Notes in Math., 949 (1982), 87-121, Springer-Verlag.

See also

  • Part II: Gen-ichi Oshikiri. Totally geodesic foliations and Killing fields, II. Tohoku Math. J., Volume 38, Number 3 (1986), pp. 351-356.