Ricci-Calculus An Introduction to Tensor Analysis and Its Geometrica
This is an entirely new book. The first edition appeared in 1923 and at that time it was up to date. But in 193 5 and 1938 the author and Prof. D. J. STRUIK published a new book, their Einführung I and li, and this book not only gave the first systematic
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MATHEM ATISCHE N WISSEN SCHAFT EN IN EINZELDARSTELLUN GEN MIT BESONDERER BERUCKSICHTIGUNG DER ANWENDUNGSGEBIET E HERAUSGEGEBEN VON
R. GRAMMEL. E. HüPF. H. HüPF. F. RELLICH F. K. SCHMIDT. B. L. VAN DER WAERDEN VOLUME X
RICCI-CALCULUS AN INTRODUCTION TO TENSOR ANALYSIS AND ITS GEOMETRICAL APPLICATIONS BY
J. A. SCHOUTEN SECOND EDITION
SPRINGER-VERLAG BERLIN HEIDELBERG GMBH 1954
RICCI-CALCULUS AN INTRODUCTION TO TENSOR ANALYSIS AND ITS GEOMETRICAL APPLICATIONS
BY
J. A. SCHOUTEN EMERITUS PROFESSOR OF MATHEMATICS IN THE UNlVERS!TY OF AMSTERDAM DIRECTOR OF THE MATHEMATICAL CENTRE AT AMSTERDAM
SECOND EDITION
WITH 16 FIGURES
SPRINGER-VERLAG BERLIN HEIDELBERG GMBH 1954
ISBN 978-3-642-05692-5 ISBN 978-3-662-12927-2 (eBook) DOI 10.1007/978-3-662-12927-2 ALLE RECHTE, INSBESONDERE DAS DER ÜBERSETZUNG IN FREMDE SPRACHEN VORBEHALTEN OHNE AUSDRÜCKLICHE GENEHMIGUNG DES VERLAGES IST ES AUCH NICHT GESTATTET, DIESES BUCH ODER TEILE DARAUS AUF PHOTOMECHANISCHEM WEGE (PHOTOKOPIE, MIKROKOPIE) ZU VERVIELFALTIGEN COPYRIGHT 1954 BY SPRINGER-VERLAG BERLIN HEIDELBERG URSPRÜNGLICHERSCHIENENBEI SPRINGER-VERLAG OHG. IN BERLIN, GÖTTINGEN AND HEIDELBERG I954 SOFTCOVER REPRINT OF THE HARDCOVER 2ND EDITION I954
This book is dedicated to the memory of
DR. GREGORIO RICCI CURBASTRO in life Professor of Mathematics in the University of Padua, who laid the foundations of tensor calculus.
Preface to the second edition. This is an entirely new book. The first edition appeared in 1923 and at that time it was up to date. But in 193 5 and 1938 the author and Prof. D. J. STRUIK published a new book, their Einführung I and li, and this book not only gave the first systematic introduction to the kernelindex method but also contained many notions that had come into prominence since 1923. For instance densities, quantities of the second kind, pseudo-quantities, normal Coordinates, the symbolism of exterior forms, the LIE derivative, the theory of variation and deformation and the theory of subprojective connexions were included. Now since 1938 there have been many new developments and so a book on RICCI calculus and its applications has to cover quite different ground from the book of 1923. Though the purpose remains to make the reader acquainted with RICCI's famous instrument in its modern form, the book must have quite a different methodical structure and quite different applications have to be chosen. The first chapter contains algebraical preliminaries but the whole text is modernized and there is a section on hybrid quantities (quantities with indices of the first and of the second kind) and one on the many abridged notations that have been developed by several authors. In the second chapter the most important analytical notions that come before the introduction of a connexion aredealt with in full. The theory of integrability and PFAFF's problern are treated here and do not get a chapter of their own this time as they did in the first edition because ScHOUTEN and v. D. KuLK's book on PFAFF's problern of 1949 can be referred to. A special sec
