Journal of the Mathematical Society of Japan

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

Koji TOJO

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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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1145287092

Digital Object Identifier
doi:10.2969/jmsj/1145287092

Mathematical Reviews number (MathSciNet)
MR2204564

Zentralblatt MATH identifier
1097.53039

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 17B70: Graded Lie (super)algebras 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

Keywords
3-symmetric space graded Lie algebra totally geodesic submanifold affine Lie algebra

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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