Journal of Differential Geometry

Submanifolds and special structures on the octonians

Robert L. Bryant

Full-text: Open access

Article information

J. Differential Geom., Volume 17, Number 2 (1982), 185-232.

First available in Project Euclid: 25 June 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]
Secondary: 22E99: None of the above, but in this section 53C40: Global submanifolds [See also 53B25]


Bryant, Robert L. Submanifolds and special structures on the octonians. J. Differential Geom. 17 (1982), no. 2, 185--232. doi:10.4310/jdg/1214436919.

Export citation


  • [1] R. Bryant, S. S. Chern and P. A. Griffiths, Notes on exterior differential systems, preprint.
  • [2] E. Calabi, Construction and properties of some 6-dimensional almost complex manifolds, Trans. Amer. Math. Soc. 87 (1958) 407-438.
  • [3] E. Cartan, La theorie des groupes finis et continus et la geometrie differentielle, Gauthier-Villars, Paris, 1937.
  • [4] E. Cartan, Les systemes differentiel esterieurs, Hermann, Paris, 1945.
  • [5] E. Cartan, Sur les systemes en involution d'equations aux derivees partielles du second ordre a une fonction inconnue de trois variables independantes, Oeuvres Completes, Vol. 2, Pt. 2, pp. 1035-1125.
  • [6] E. Cartan, Uber die Einfachen Transformationsgruppen, Oeuvres Completes, Vol. 1, Pt. 1, pp. 107-132.
  • [7] S. S. Chern, Minimal surfaces in an Euclidean space of N dimensions, Differential and Combinatorial Topology (Morse Jubilee Volume), Princeton Univ. Press, Princeton, NJ, 1965, pp. 187-198.
  • [8] S. S. Chern, Complex manifolds without potential theory, 2nd Ed. Springer-Verlag, Berlin and New York, 1979.
  • [9] T. Fukami and Ishihara, Almost Hermitian structure on S6, Tohoku Math. J. (2) 7 (1955) 151-156.
  • [10] A. Gray, Vector cross products on manifolds, Trans. Amer. Math. Soc. 141 (1969) 465-504 (and references cited therein).
  • [11] G. Griffiths and J. Harris, Principles of algebraic geometry, Wiley-Interscience, New York.
  • [12] R. Harvey and B. Lawson, Calibrated geometries, preprint.
  • [13] S. Koto, Some theorems on almost Kahlerian spaces, J. Math. Soc. Japan 12 (1960) 422-433.
  • [14] N. Steenrod, The topology of fiber bundles, Princeton Math. Ser. Princeton Univ. Press, Princeton, NJ.
  • [15] R. Wells, Differential analysis on complex manifolds, Springer-Verlag, Berlin and New York, 1979.