Ricci Calculus

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.

Ricci Calculus

Author: Jan Arnoldus Schouten

Publisher: Springer Science & Business Media

ISBN: 3662129272

Page: 514

View: 329

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 kernel index 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 cal culus 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 applica tions 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.

Encyclopaedia of Mathematics

Tensor calculus is an important constituent part of the apparatus of differential
geometry. In this connection it was first systematically developed by G. Ricci and
T. Levi-Civita (see [I]): it has often been called the 'Ricci calculus". The term '
tensor* ...

Encyclopaedia of Mathematics

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 9781556080081

Page: 536

View: 481

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

The Attraction of Gravitation

to call attention to "Ricci's generally neglected absolute calculus and to its
suggestiveness as an implement of research in developing the theory of surfaces
of two dimensions in Euclidean space of n dimensions" (Wilson 1916). During
this ...

The Attraction of Gravitation

Author: John Earman

Publisher: Springer Science & Business Media

ISBN: 9780817636241

Page: 432

View: 527

Devoted to the history of general relativity, this text provides reviews from scholars all over the world. Many of the papers originated at the Third International Conference on the History of General Relativity, held at the University of Pittsburgh in the summer of 1991. Topics covered include: disputes with Einstein; the empirical basis of general relativity; variational principles in general relativity; the reception and development of general relativity; and cosmology and general relativity.

Tensor Analysis and Nonlinear Tensor Functions

In his works , in 1886-1901 Ricci created a new apparatus called the absolute
differential calculus for algebraic and differential operations on covariant and
contravariant systems of order 1 ( so Ricci named tensor components by Irira ... ry
and ...

Tensor Analysis and Nonlinear Tensor Functions

Author: Yuriy I. Dimitrienko

Publisher: Springer Science & Business Media

ISBN: 9781402010156

Page: 662

View: 220

Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc. The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time. It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua. The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science.

The Ricci Flow

http://dx.doi.org/10.1090/surv/110/10 APPENDIX A The Ricci calculus From the
viewpoint of Riemannian geometry, the Ricci flow is a very natural evolution
equation, because it can be formulated entirely in terms of intrinsically-defined ...

The Ricci Flow

Author: Bennett Chow

Publisher: American Mathematical Soc.

ISBN: 0821835157

Page: 325

View: 639

The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to 'flow' a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics. Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program. The Ricci flow method is now central to our understanding of the geometry and topology of manifolds.This book is an introduction to that program and to its connection to Thurston's geometrization conjecture. The authors also provide a 'Guide for the hurried reader', to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called 'fast track'. The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds. ""The Ricci Flow"" was nominated for the 2005 Robert W. Hamilton Book Award, which is the highest honor of literary achievement given to published authors at the University of Texas at Austin.

Tensor Calculus

G . Ricci and T . LEVI - CIVITA , Méthodes de calcul differentiel absolu et leurs
applications ( Paris , 1923 ) . ( Reprinted from Mathematische Annalen , tome 54 ,
1900 . ) 2 . J . A . SCHOUTEN , Ricci Calculus ( 2nd ed . , Berlin , 1954 ) . 3 .

Tensor Calculus

Author: John Lighton Synge

Publisher:

ISBN:

Page: 324

View: 347

Zeitschrift f r Astrophysik

X . Band : Ricci - Calculus . An Introduction to Tensor Analysis and its
Geometrical Applications . By J . A . Schouten , emeritus Professor of
Mathematics in the University of Amsterdam , Director of the Mathematical Centre
at Amsterdam .

Zeitschrift f  r Astrophysik

Author:

Publisher:

ISBN:

Page:

View: 552

Encyclopedia of physics

[ 19 ] SCHOUTEN , J . A . : Der Ricci - Kalkül . Berlin 1924 . [ 20 ] SCHOUTEN , J .
A . : Tensor analysis for Physicists . Oxford 1954 . [ 21 ] SCHOUTEN , J . A . : Ricci
Calculus . Berlin 1954 . [ 22 , 23 ) SPERNER , E . : Einführung in die analytische ...

Encyclopedia of physics

Author:

Publisher:

ISBN:

Page:

View: 592

Mathematische Methoden

[ 19 ] SCHOUTEN , J. A .: Der Ricci - Kalkül . Berlin 1924 . [ 20 ] SCHOUTEN , J. A
.: Tensor analysis for Physicists . Oxford 1954 . [ 21 ] SCHOUTEN , J. A .: Ricci
Calculus . Berlin 1954 . [ 22 , 23 ] SPERNER , E .: Einführung in die analytische ...

Mathematische Methoden

Author:

Publisher:

ISBN:

Page: 364

View: 145

Annales Academiae Scientiarum Fennicae

[ 9 ] SCHOUTEN , J . A . : Ricci - calculus . An introduction to tensor analysis and
its geo - . metrical applications . - 2 . Aufl . , Grundlehren der mathematischen
Wissenschaften X , Springer - Verlag , Berlin Göttingen / Heidelberg , 1954 .

Annales Academiae Scientiarum Fennicae

Author:

Publisher:

ISBN:

Page:

View: 945

The Hutchinson Dictionary of Scientists

The Hutchinson Dictionary of Scientists

Author:

Publisher:

ISBN:

Page: 552

View: 592

A comprehensive dictionary of scientific facts. It contains the biographies of numerous scientists including the Nobel prize winners; the discoveries of each one; the importance of their specialities and how they set about their work; and also what drove and inspired them as human beings.

Commentationes Physico mathematicae

1950 [ 8 ] KUSTAANHEIMO , P .: An axiomatic definition of the tensor calculus -
Intern . Math . ... [ 9 ] - » - On the equivalence of some calculi of transformable
quantities Sc . Fenn . Comm . ... 1921 . [ 18 ] SCHOUTEN , J. A .: Ricci - calculus .

Commentationes Physico mathematicae

Author:

Publisher:

ISBN:

Page:

View: 277

The Italian Achievement

529 In 1930 , G. TONELLI ( born Gallipoli ) , L. CESARI and E. DIGIORGI were
the first to study multiple integral surfaces . 522/23 In 1880 , Gregorio RICCI (
born Lugo ) developed absolute differential calculus , called after him Ricci
Calculus .

The Italian Achievement

Author: Arturo Barone

Publisher: Renaissance Books

ISBN:

Page: 324

View: 217

This book is an A to Z of over one thousand "firsts" achieved by Italians in almost every aspect of life during the last millennium--from fashion and food to flying and photography; from art and design to painting and sailing; from motor cars to musical instruments; from philosophy to physics; from clocks to computers.