Holomorphic Riemannian metrics on compact threefolds are locally homogeneous (Q2372813)
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scientific article
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| English | Holomorphic Riemannian metrics on compact threefolds are locally homogeneous |
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Holomorphic Riemannian metrics on compact threefolds are locally homogeneous (English)
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1 August 2007
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The author studies complex connected compact 3-manifolds admitting a holomorphic Riemannian metric. He shows that such a manifold is locally homogeneous. Examples of such manifolds were presented in [\textit{E. Ghys}, J. Reine Angew. Math. 468, 113--138 (1995; Zbl 0868.32023)]. The paper is a continuation of the research gives in [Ann. Inst. Fourier 51, No. 6, 1663--1690 (2001; Zbl 1016.53051)]. The proof uses methods of analytic geometry, invariant theory for algebraic actions and Gromov's rigid geometric structures.
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holomorphic Riemannian metric
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locally homogeneous
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complex 3-manifold
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3-fold
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