Tohoku Mathematical Journal
2008
December
SECOND SERIES VOL. 60, NO. 4

Tohoku Math. J.
60 (2008), 549-580

Title COMPLEX STRUCTURES, TOTALLY REAL AND TOTALLY GEODESIC SUBMANIFOLDS OF COMPACT 3-SYMMETRIC SPACES, AND AFFINE SYMMETRIC SPACES

Author Koji Tojo

(Received March 16, 2007, revised April 21, 2008)
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.

2000 Mathematics Subject Classification. Primary 53C40; Secondary 17B70, 53C30.
Key words and phrases. 3-symmetric space, graded Lie algebra, totally geodesic submanifold, affine symmetric space.

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