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CLASSIFICATION OF PARA-REAL FORMS OF ABSOLUTELY SIMPLE PARA-HERMITIAN SYMMETRIC SPACES

Sugimoto, Kyoji 大阪大学 DOI:10.18910/88487

2022.07

概要

Let G/L be a para-Hermitian symmetric space and let I be its para-complex structure. We will introduce the notion of para-real forms of para-Hermitian symmetric spaces. A nonempty set R ⊂ G/L is called a para-real form, if there exists an involutive isometry Ξ of G/L such that Ξ is a para-antiholomorphic and that R coincides with a connected component of (G/L) Ξ Fix(G/L, Ξ). In addition, two para-real forms R1 of G/L1 and R2 of G/L2 are equivalent, if there exists a homothety Φ from G/L1 onto G/L2 such that Φ is para-holomorphic and that Φ(R1) = R2. We assume that the complexification of the Lie algebra g of G is simple and G/L can be realized as a hyperbolic orbit under the adjoint representation of G on the Lie algebra g of G. The main result of this paper is the following theorem:

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参考文献

[1] M. Berger: Les espaces sym´etriques noncompacts, Ann. Sci. Ecole Norm. Sup. ´ 74 (1957), 85–177.

[2] N. Boumuki: The classification of real forms of simple irreducible pseudo-Hermitian symmetric spaces, J. Math. Soc. Japan 66 (2014), 37–88.

[3] S. Helgason: Differential Geometry, Lie groups, and Symmetric Spaces, Amer. Math. Soc., Providence, RI, 2001.

[4] S. Kaneyuki: On classification of para-Hermitian symmetric spaces, Tokyo J. Math. 8 (1985), 473–482.

[5] S. Kaneyuki: On orbit structure of compactifications of para-Hermitian symmetric spaces, Japan J. Math. (N.S.) 13 (1987), 333–370.

[6] S. Kaneyuki and M. Kozai: Paracomplex structures and affine symmetric spaces, Tokyo J. Math. 8 (1985), 81–98.

[7] S. Kaneyuki and M. Kozai: On isotropy subgroup of the automorphism group of a para-Hermitian symmetric space, Tokyo J. Math. 8 (1985), 483–490.

[8] S. Kobayashi and K. Nomizu: Foundations of Differential Geometry. Vol. I, Interscience Publishers, a Division of John Wiley & Sons, New York, London, 1963.

[9] S.S. Koh: On affine symmetric spaces, Trans. Amer. Math. Soc. 119 (1965), 291–309.

[10] D.S.P. Leung: Reflective submanifolds. IV. Classification of real forms of Hermitian symmetric spaces, J. Differential Geom. 14 (1979), 179–185.

[11] O. Loos: Symmetric Spaces. I: General Theory, Benjamin Inc., New York-Amsterdam, 1969.

[12] S. Murakami: Sur la classification des alg´ebres de Lie r´eelles et simples, Osaka J. Math. 2 (1965), 291–307.

[13] T. Noda and N. Boumuki: On relation between pseudo-Hermitian symmetric pairs and para-Hermitian symmetric pairs, Tohoku Math. J. 61 (2009), 67–82.

[14] K. Nomizu: On the group of affine transformations of an affinely connected manifold, Proc. Amer. Math. Soc. 4 (1953), 816–823.

[15] K. Nomizu: Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33–65.

[16] T. Oshima and J. Sekiguchi: The restricted root system of a semisimple symmetric pair; in Group Representations and Systems of Differential Equations (Tokyo, 1982), Adv. Stud. Pure Math. 4, North-Holland, Amsterdam, 1984, 433–497.

[17] W. Rossmann: The structure of semisimple symmetric spaces, Canad. J. Math. 31 (1979), 157–180.

[18] T. Shimokawa and K. Sugimoto: On the groups of isometries of simple para-Hermitian symmetric spaces, Tsukuba J. Math. 41 (2017), 21–42.

[19] M. Takeuchi: Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tohoku Math. J. 36 (1984), 293–314.

[20] I. Yokota: Realizations of involutive automorphisms σ and Gσ of exceptional linear Lie groups G, part I, G = G2, F4, and E6, Tsukuba J. Math. 14 (1990), 185–223.

[21] I. Yokota: Realizations of involutive automorphisms σ and Gσ of exceptional linear Lie groups G, part II, G = E7, Tsukuba J. Math. 14 (1990), 379–404.

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