Isometries of Hermitian symmetric spaces

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Every symmetric R-space is realized as a real form of a Hermitian symmetric space of compact type and vice- versa (Takeuchi 1984). Here a real form of a Hermitian symmetric space M is the fixed point set of an involutive anti-holomorphic isometry of M. Every real form is connected and a totally geodesic Lagrangian submanifold of M. 4
M : a Riemannian manifold τ : an involutive isometry of M A connected component of F (τ, M) := {x ∈ M | τ(x) = x} is called a reflective submanifold. Reflective submanifolds in simply connected irreducible Riemannian symmetric spaces of compact type are clas- sified by Leung (1974, ’75 and ’79). 5
Page 1 and 2: Isometries of Hermitian symmetric s
Page 3: 1. Introduction A Riemannian symmet
Page 7 and 8: 2. Extrinsically symmetric spaces M
Page 9 and 10: P = G/K : a Riemannian symmetric sp
Page 11 and 12: I(M) : the group of isometries of M
Page 13 and 14: 3. Isometries of Hermitian symmetri
Page 15 and 16: Consider the map ι : P → g, p
Page 17 and 18: Proof: P = P1 × · · · × Pr : a
Page 19 and 20: Let f ∈ I(P ). Let m be the midpo
Page 21 and 22: Lemma (I f)∗(Jo) ∈ {±Jo}. Proo
Page 23 and 24: Remark It is a known fact that ever
Page 25 and 26: 4. Another result Theorem 2 (Loos 1
Page 27 and 28: Proposition 3 Let M be a compact Ri
Page 29: Further, a meridian M − of X is e

Isometries of Hermitian symmetric spaces

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