Journal of the Mathematical Society of Japan

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


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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

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

First available in Project Euclid: 17 April 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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