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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 25, Issue 2 (Mar 2013)


Complex Osserman Kähler manifolds in dimension four

Miguel Brozos-Vázquez
  • Mathematics Department, E. U. Politécnica, University of A Coruña, 15405 Ferrol, Spain
  • Email:
/ Peter Gilkey
  • Mathematics Department, University of Oregon, Eugene OR 97403, USA
  • Email:
Published Online: 2013-03-01 | DOI: https://doi.org/10.1515/form.2011.119


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

About the article

Received: 2010-04-05

Published Online: 2013-03-01

Published in Print: 2013-03-01

Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.119.

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© 2013 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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