Tohoku Mathematical Journal

Complex structures, totally real and totally geodesic submanifolds of compact 3-symmetric spaces, and affine symmetric spaces

Koji Tojo

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Abstract

We construct invariant complex structures of a compact 3-symmetric space by means of the canonical almost complex structure of the underlying manifold and some involutions of a Lie group. Moreover, by making use of graded Lie algebras and some invariant structures of affine symmetric spaces, we classify half dimensional, totally real and totally geodesic submanifolds of a compact 3-symmetric space with respect to each invariant complex structure.

Article information

Source
Tohoku Math. J. (2), Volume 60, Number 4 (2008), 549-580.

Dates
First available in Project Euclid: 19 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1232376166

Digital Object Identifier
doi:10.2748/tmj/1232376166

Mathematical Reviews number (MathSciNet)
MR1808645

Zentralblatt MATH identifier
1180.53054

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 symmetric space

Citation

Tojo, Koji. Complex structures, totally real and totally geodesic submanifolds of compact 3-symmetric spaces, and affine symmetric spaces. Tohoku Math. J. (2) 60 (2008), no. 4, 549--580. doi:10.2748/tmj/1232376166. https://projecteuclid.org/euclid.tmj/1232376166


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