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The Petrov classification is an important algebraic classification for the Weyl tensor valid in 4-dimensional space-times. In this book such classification is generalized to manifolds of arbitrary dimension and signature. This is accomplished by interpreting the Weyl tensor as a linear operator on the bundle of p-forms and computing the Jordan canonical form of this operator. Throughout this work the spaces are assumed to be complexified, so that different signatures correspond to different reality conditions, providing a unified treatment. A higher-dimensional generalization of the so-called self-dual manifolds is also investigated. The most important result related to the Petrov classification is the Goldberg-Sachs theorem. Here are presented two partial generalizations of such theorem valid in even-dimensional manifolds. On the pursuit of these results the spinorial formalism in 6 dimensions was developed from the very beginning. The book is intended to be self-contained at the level of a graduate student of physics or mathematics, with an introductory chapter about general relativity and appendices introducing Clifford algebra, spinors and group representation theory.
About the author
Professor Adjunto da UFPR. Tem experiência na área de Física, atuando principalmente nos seguintes temas: caos, sincronização, redes neurais, redes e simulações numéricas.
