The Gel′fand theorem and its converse for Kähler manifolds

Kowalski, O.; Vanhecke, L.

doi:10.1090/S0002-9939-1988-0915734-4

The Gel′fand theorem and its converse for Kähler manifolds
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by O. Kowalski and L. Vanhecke PDF

Proc. Amer. Math. Soc. 102 (1988), 150-152 Request permission

Abstract:

We characterize the locally Hermitian symmetric manifolds among the homogeneous Kähler manifolds $M$ by each of the following properties: (i) all ${A_0}(M)$-invariant differential operators on $M$ commute $({A_0}(M)$ denotes the identity component of the group of all holomorphic isometries); (ii) all geodesies are orbits of one-parameter groups of holomorphic isometries.

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