Isometries of Hermitian symmetric spaces

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Theorem (Ferus 1974, Eschenburg-Heintze 1995) Every symmetric R-space is extrinsically symmetric and every full compact extrinsically symmetric submanifold of Euclidean space is a symmetric R-space. 8
P = G/K : a Riemannian symmetric space of compact type G = I0(M), K = {g ∈ G | g(o) = o}, o ∈ P g = k ⊕ p : the canonical decomposition g = Lie(G), k = Lie(K), p ∼ = ToP Take ξ(̸= 0) ∈ p with ad(ξ) 3 = −ad(ξ), then M = Ad G(K)ξ ⊂ p : a symmetric R-space 9
Page 1 and 2: Isometries of Hermitian symmetric s
Page 3 and 4: 1. Introduction A Riemannian symmet
Page 5 and 6: M : a Riemannian manifold τ : an i
Page 7: 2. Extrinsically symmetric spaces M
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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