Global rigidity of holomorphic Riemannian metrics on compact complex 3-manifolds |
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Authors: | Sorin Dumitrescu and Abdelghani Zeghib |
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Institution: | (1) Département de Mathématiques d’Orsay, équipe de Topologie et Dynamique, Bat. 425, UMR 8628 CNRS, Univ. Paris-Sud (11), 91405 Orsay Cedex, France;(2) CNRS, UMPA, école Normale Supérieure de Lyon, 46 allée d’Italie, 69364 Lyon Cedex 07, France |
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Abstract: | We study compact complex 3-manifolds M admitting a (locally homogeneous) holomorphic Riemannian metric g. We prove the following: (i) If the Killing Lie algebra of g has a non trivial semi-simple part, then it preserves some holomorphic Riemannian metric on M with constant sectional curvature; (ii) If the Killing Lie algebra of g is solvable, then, up to a finite unramified cover, M is a quotient Γ\G, where Γ is a lattice in G and G is either the complex Heisenberg group, or the complex SOL group.
S. Dumitrescu was partially supported by the ANR Grant BLAN 06-3-137237. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 53B21 53C56 53A55 |
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