Characteristic Classes and Weyl Tensor: Applications to General Relativity
- 1 June 1970
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 66 (2) , 265-268
- https://doi.org/10.1073/pnas.66.2.265
Abstract
In a recent paper, Chern and Simons proved that the Pontrjagin forms of a Riemannian manifold remain invariant under a conformal deformation. We show that these forms can be expressed uniquely in terms of the conformal curvature tensor: this provides a new proof of their result. Similar techniques can be applied to Euler-Poincare characteristic class, as suggested to me by A. Taub. We obtain the following: If the Weyl tensor of a compact space time is of type III of Bel-Petrov, then it cannot carry a perfect fluid + electromagnetic field.Keywords
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