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Forum Mathematicum

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Complex Osserman Kähler manifolds in dimension four

1Mathematics Department, E. U. Politécnica, University of A Coruña, 15405 Ferrol, Spain

2Mathematics Department, University of Oregon, Eugene OR 97403, USA

Citation Information: Forum Mathematicum. Volume 25, Issue 2, Pages 313–336, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/form.2011.119, March 2013

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Let be a 4-dimensional almost-Hermitian manifold which satisfies the Kähler identity. We show that is complex Osserman if and only if has constant holomorphic sectional curvature. We also classify in arbitrary dimensions all the complex Osserman Kähler models which do not have three eigenvalues.

Keywords: Complex Osserman model; Jacobi operator; Kähler manifold; Osserman conjecture

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