ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53 S.entürk, Zerrin, Istanbul Technical University, TURKEY On a Certain Application of the Patterson’s Curvature Identity In this work, we investigate arbitrary 4-dimensional semi-Riemannian manifolds fulfilling the condition“the tensors R · C and Q(S, C) are linearly dependent”. We consider 4-dimensional manifolds satisfying the equality Q(S, C = 0 and we prove that such manifolds are semisymmetric and their scalar curvature is equal to zero. Finally, we describe an example of a manifold having all these properties. Part of these results is joint work with R. Deszcz and M. Hotloś. Reference: E. M. Patterson, A class of critical Riemannian metrics, J. London Math. Soc. 2, 23 (1981), 349–358.