Blažić, Novica Conformally Osserman Lorentzian manifolds. (English) Zbl 1143.53336 Kragujevac J. Math. 28, 87-96 (2005). A pseudo-Riemannian manifold \(M\) is conformally flat if the eigenvalues of the symmetric Weyl Jacobi operator, \(J_W(x)y=W(y,x)x\) (\(W(x,y)\) being the standard Weyl conformal curvature operator), has constant eigenvalues on the bundle of unit time-like (space-like) vectors. The author studies conformal Osserman Lorentzian manifolds. The main result is the following characterization: if \(M\) is a Lorentzian manifold of dimension \(n>3\), then it is a conformal Osserman manifold if and only if it is a conformally flat manifold. This result shows some rigidity of the Lorentzian signature, which is illustrated by some recent results concerning conformal Osserman manifolds in other signatures (Section 4). Reviewer: Zoran Rakić (Beograd) MSC: 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics Keywords:time-like vectors; space-like vectors; Jacobi operator; Osserman manifold; Weyl conformal tensor; conformally flat PDFBibTeX XMLCite \textit{N. Blažić}, Kragujevac J. Math. 28, 87--96 (2005; Zbl 1143.53336)