Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

HYPERSURFACES IN A 6-DIMENSIONAL SPHERE

  • Published : 1997.02.01
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Abstract

A 6-dimensional sphere considered as a homogeneous space $G_2/SU(3)$ where $G_2$ is the group of automorphism of the octonians O. From this representation, we can define an almost comlex structure on a 6-dimensional sphere by making use of the vector cross product of the octonians. Also it is known that a homogeneous space $G_2/U(2)$ coincides with the Grassmann manifold of oriented 2-planes of a 7-dimensional Euclidean space.

Keywords

References

  1. J. Diff. Geom v.17 Submanifolds and special structures on the octonians R. L. Bryant
  2. Submanifolds and isometric immersions M. Dajczer
  3. Kodai Math. J. v.16 Characteristic classes of oriented 6-dimensional submanifolds in the octonians H. Hashimoto
  4. J. Korean Math, Soc. v.28 Oriented 5-dimensional submanifolds in the purely imaginary octonians H. Hashimoto