Tohoku Mathematical Journal

Totally real totally geodesic submanifolds of compact 3-symmetric spaces

Koji Tojo

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Abstract

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

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

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178207535

Digital Object Identifier
doi:10.2748/tmj/1178207535

Mathematical Reviews number (MathSciNet)
MR1808645

Zentralblatt MATH identifier
1026.53030

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

Citation

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. https://projecteuclid.org/euclid.tmj/1178207535


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