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The Gelfand theorem and its converse for Kähler manifolds

Authors: O. Kowalski and L. Vanhecke
Journal: Proc. Amer. Math. Soc. 102 (1988), 150-152
MSC: Primary 53C30,; Secondary 32M05,53C55
MathSciNet review: 915734
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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.

References [Enhancements On Off] (What's this?)

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Keywords: Invariant differential operator, Hermitian symmetric space, homogeneous Kähler manifold
Article copyright: © Copyright 1988 American Mathematical Society

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