Lichnerowicz A. Elements of Tensor Calculus

Methuen & Co. Ltd., 1962. — 164 p.In 1900 Ricci and Levi-Civita produced a celebrated memoire which gave the first systematic account of tensor calculus and drew the attention of mathematicians and physicists to some of its applications. Since then much has happened. The appearance of the theory of relativity, which would not have been possible without the previous existence of tensor calculus, gave it, in turn, an immense impetus. Tensor calculus has now become one of the essential techniques of modern theoretical physics. It has even been used recently in the study of technical problems such as the interconnection of electrical machines. It can be said that tensor calculus now forms a fundamental part of mathematics and physics.This little book is divided into two parts, one concerned with tensor algebra and analysis, the other with the most important applications. In Part I the study of tensor algebra ends with a brief consideration of outer product algebras, since this technique deserves to be better known by physicists. On the other hand, the concept of tensor density, which is of little mathematical interest, is not introduced. This concept is, in fact, easily avoided by the introduction of adjoint tensors of antisymmetric tensors.