Exact solutions of Bianchi I spacetimes which admit Conformal Killing Vectors

We develop a new method in order to classify the Bianchi I spacetimes which admit Conformal Killing Vectors (CKVs). The method is based on two propositions which relate the CKVs of 1+(n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+(\text {n}-1)$$\end{document} decomposable Riemannian spaces with the CKVs of the (n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\text {n}-1)$$\end{document} subspace and show that if 1+(n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+(\text {n}-1)$$\end{document} space is conformally flat then the (n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\text {n}-1)$$\end{document} spacetime is maximally symmetric. The method is used to study the conformal algebra of the Kasner spacetime and other less known Bianchi type I matter solutions of General Relativity.