Tohoku Mathematical Journal

Totally real totally geodesic submanifolds of compact 3-symmetric spaces

Koji Tojo

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We prove that a half dimensional, totally real and totally geodesic submanifold of a compact Riemannian 3-symmetric space is expressed as an orbit of a Lie subgroup of the isometry group of the ambient manifold. Moreover, we associate such submanifolds with graded Lie algebras of the second kind.

Article information

Tohoku Math. J. (2), Volume 53, Number 1 (2001), 131-143.

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

Primary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
Secondary: 17B20: Simple, semisimple, reductive (super)algebras


Tojo, Koji. Totally real totally geodesic submanifolds of compact 3-symmetric spaces. Tohoku Math. J. (2) 53 (2001), no. 1, 131--143. doi:10.2748/tmj/1178207535.

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