## Tohoku Mathematical Journal

### Complex structures, totally real and totally geodesic submanifolds of compact 3-symmetric spaces, and affine symmetric spaces

Koji Tojo

#### Abstract

We construct invariant complex structures of a compact 3-symmetric space by means of the canonical almost complex structure of the underlying manifold and some involutions of a Lie group. Moreover, by making use of graded Lie algebras and some invariant structures of affine symmetric spaces, we classify half dimensional, totally real and totally geodesic submanifolds of a compact 3-symmetric space with respect to each invariant complex structure.

#### Article information

Source
Tohoku Math. J. (2), Volume 60, Number 4 (2008), 549-580.

Dates
First available in Project Euclid: 19 January 2009

https://projecteuclid.org/euclid.tmj/1232376166

Digital Object Identifier
doi:10.2748/tmj/1232376166

Mathematical Reviews number (MathSciNet)
MR1808645

Zentralblatt MATH identifier
1180.53054

#### Citation

Tojo, Koji. Complex structures, totally real and totally geodesic submanifolds of compact 3-symmetric spaces, and affine symmetric spaces. Tohoku Math. J. (2) 60 (2008), no. 4, 549--580. doi:10.2748/tmj/1232376166. https://projecteuclid.org/euclid.tmj/1232376166

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