Mathematical Physics

In the following six Sections, the author studied a number of topics dealing with tensor calculus, following closely the text T. Levi-Civita, Lezioni di calcolo differenziale assoluto (Stock, Rome, 1925), which was present in the Majorana personal library. For the notations used and further comments on the topics treated, we refer the reader to this book (we denote it as Levi-Civita I) or to its English translation (denoted as Levi-Civita E) in T. Levi-Civita, The Absolute Differential Calculus – Calculus of Tensors (Blackie & Son, London, 1926). Some explicit references to chapters (III and IV) or pages (pp. 48, 60, 123, 137, 140, 141, 143, 160, 173, 174, 178, 197 of Levi-Civita I or pp. 36, 47, 107, 119, 121, 123, 131, 140, 152, 153, 156, 172 of Levi-Civita E) of this book are reported throughout the manuscript. A few results, on the contrary, do not appear in the mentioned book; they were obtained by Majorana, or he simply reported what was expounded in the university course taught by Levi-Civita at the University of Rome and followed by Majorana himself.