Vol. 245, No. 2, 2010

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ISSN: 0030-8730
Conformally Osserman manifolds

Yuri Nikolayevsky

Vol. 245 (2010), No. 2, 315–358
Abstract

An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally Osserman if its Weyl conformal curvature tensor at every point is Osserman. We prove that a conformally Osserman manifold of dimension n3,4,16 is locally conformally equivalent either to a Euclidean space or to a rank-one symmetric space.

Keywords
Osserman manifold, Weyl tensor, Jacobi operator, Clifford structure
Mathematical Subject Classification 2000
Primary: 53B20, 53A30
Milestones
Received: 31 January 2009
Accepted: 20 May 2009
Published: 1 April 2010
Authors
Yuri Nikolayevsky
Department of Mathematics and Statistics
La Trobe University
Melbourne, Victoria 3086
Australia