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Graham Hall

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In this talk I will discuss the Weyl conformal and projective tensors, C and W, and summarise their properties, for example (Weyl’s theorems) that two conformally related metrics have the same Weyl conformal tensor and that two projectively related connections have the same Weyl projective tensor. Then I will explain the (almost complete) failure of any such converse theorems. Next I will discuss several ways of describing conformal and projective structure in terms of C, W and their symmetries and show that, for each structure, no two of them are equivalent. Then the properties of C and W under manifold products will be explained. Finally, I will review some recent results about projective relatedness and describe how to evaluate the condition that two space-times have the same projective tensor.

This talk is part of the DAMTP Friday GR Seminar series.

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