Conformally Osserman manifolds

Yuri Nikolayevsky

Vol. 245 (2010), No. 2, 315–358

DOI: 10.2140/pjm.2010.245.315

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 n≠3,4,16 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