Год выпуска: 2014 Автор: Carlos Batista Издательство: LAP Lambert Academic Publishing Страниц: 208 ISBN: 9783659520655
Описание
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...
