## Journal of the Mathematical Society of Japan

### Classification of totally real and totally geodesic submanifolds of compact 3-symmetric spaces

Koji TOJO

#### Abstract

It is known that each 3-symmetric space admits an invariant almost complex structure $J$, so-called a canonical almost complex structure. By making use of simple graded Lie algebras and an affine Lie algebra, we classify half dimensional, totally real (with respect to $J$) and totally geodesic submanifolds of compact 3-symmetric spaces.

#### Article information

Source
J. Math. Soc. Japan, Volume 58, Number 1 (2006), 17-53.

Dates
First available in Project Euclid: 17 April 2006

https://projecteuclid.org/euclid.jmsj/1145287092

Digital Object Identifier
doi:10.2969/jmsj/1145287092

Mathematical Reviews number (MathSciNet)
MR2204564

Zentralblatt MATH identifier
1097.53039

#### Citation

TOJO, Koji. Classification of totally real and totally geodesic submanifolds of compact 3-symmetric spaces. J. Math. Soc. Japan 58 (2006), no. 1, 17--53. doi:10.2969/jmsj/1145287092. https://projecteuclid.org/euclid.jmsj/1145287092

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