Christoffel Symbols

High Quality Content by WIKIPEDIA articles! In mathematics and physics, the Christoffel symbols, named for Elwin Bruno Christoffel (1829-1900), are numerical arrays of real numbers that describe, in coordinates, the effects of parallel transport in curved surfaces and, more generally, manifolds. As such, they are coordinate-space expressions for the Levi-Civita connection derived from the metric tensor. In a broader sense, the connection coefficients of an arbitrary (not necessarily metric) affine connection in a coordinate basis are also called Christoffel symbols. The Christoffel symbols may be used for performing practical calculations in differential geometry. For example, the Riemann curvature tensor can be expressed entirely in terms of the Christoffel symbols and their first partial derivatives. Dannoe izdanie predstavlyaet soboj kompilyatsiyu svedenij, nahodyaschihsya v svobodnom dostupe v srede Internet v tselom, i v informatsionnom setevom resurse "Vikipediya" v chastnosti. Sobrannaya po chastotnym zaprosam ukazannoj tematiki, dannaya kompilyatsiya postroena po printsipu podbora blizkih informatsionnyh ssylok, ne imeet samostoyatelnogo syuzheta, ne soderzhit nikakih analiticheskih materialov, vyvodov, otsenok moralnogo, eticheskogo, politicheskogo, religioznogo i mirovozzrencheskogo haraktera v otnoshenii glavnoj tematiki, predstavlyaya soboj isklyuchitelno faktologicheskij material. This book was created using print-on-demand technology.