Hokkaido Mathematical Journal

Orthogonal almost complex structures of hypersurfaces of purely imaginary octonions

Hideya HASHIMOT and Misa OHASHI

Full-text: Open access

Abstract

First we give the new elementary proof of the structure equations of $G_2$ and the congruence theorem of hypersurfaces of the purely imaginary octonions $\ImO$ under the action of $G_2$. Next, we classify almost complex structures of homogeneous hypersurfaces of $\ImO$ into 4-types.

Article information

Source
Hokkaido Math. J., Volume 39, Number 3 (2010), 351-387.

Dates
First available in Project Euclid: 29 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1288357973

Digital Object Identifier
doi:10.14492/hokmj/1288357973

Mathematical Reviews number (MathSciNet)
MR2743828

Zentralblatt MATH identifier
1206.53057

Subjects
Primary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
octonions almost complex structure $G_2$-congruent $G_2$-orbits decomposition

Citation

HASHIMOT, Hideya; OHASHI, Misa. Orthogonal almost complex structures of hypersurfaces of purely imaginary octonions. Hokkaido Math. J. 39 (2010), no. 3, 351--387. doi:10.14492/hokmj/1288357973. https://projecteuclid.org/euclid.hokmj/1288357973


Export citation