Reviews - What do customers think about Ricci-Calculus: An Introduction to Tensor Analysis and its Geometrical Applications (Grundlehren der mathematischen Wissenschaften)?
Review of "Ricci Calculus" Jul 31, 2008
"Ricci Calculus" is the defacto standard reference for tensor transformation theory. Schouten (pronounced "Scoutin") introduces fundamental geometric quantities based on the co-and contravariant transformation rules and then systematically builds up a manifold based on invariance of these quantities. The various geometric manifolds are constructed in a systematic way, starting from rectilinear coordinates and then by introduction of the "metric," connection, curvature tensors, and so forth. The book initially appears terse but once you get the hang of it and really stick with it, the power of the notation emerges and the notation also functions as an efficient book-keeping device when doing transformation theory calculations. Often, the meaning of certain calculations are even clarified when following Schouten's approach. Although specific applications are not really discussed in this work, the book is a must-have reference for those applying tensor transformation theory in general relativity, gauge fields, continuum theory, and complex manifolds.