{"product_id":"generalizing-the-petrov-classification-von-carlos-batista","title":"Generalizing the Petrov Classification","description":"\u003cp\u003eThe 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783659520655\"\u003e\u003ch3\u003eOn the Pursuit of Generalizations for the Petrov Classification and the Goldberg-Sachs Theorem\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783659520655","offer_id":39482505068637,"sku":"9783659520655","price":41.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/0ca4f3d5-bcb9-4917-854b-1b712c461ee4.jpg?v=1773381388","url":"https:\/\/shop.autorenwelt.de\/en\/products\/generalizing-the-petrov-classification-von-carlos-batista","provider":"Autorenwelt Shop","version":"1.0","type":"link"}