Theory of Linear Connections

We ask for the linear connections associable with this configuration. It can then be shown that an infinite number of L, related by (1.1) can be obtained from this projective connection. There is a fundamental principle involved in this ...

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Author: D. J. Struik

Publisher: Springer Science & Business Media

ISBN: 9783642507991

Category: Mathematics

Page: 68

View: 887

This monograph intends to give a general survey of the different branches of the geometry of linear displacements which so far have received attention', The material on this new type of differential geometry has grown so rapidly in re cent years that it is impossible, not only to be complete, but even to do justice to the work of the different authors, so that a selection had to be made, We hope, however, that enough territory is covered to enable the reader to understand the present state of the theory in the essential points, The author wishes to thank several mathematicians who have helped hirn with remarks and suggestions; especially Dr. J.A. SCHOUTEN of Delft and Dr. N. HANSEN BALL of Princeton. Cambridge, Mass., October 1933. D.J. STRUIK. Contents. Page Introduction ... I. Algebra ... 5 1. Vectors and tensors in E n 5 2. Densities ... 6 3. Measuring vectors . 7 4. Point algebra. . . 8 5. The general manifold X" 9 6. Non-holonomic measuring vectors . 10 7. Pseudotensors ... 12 11. Affine connections ... 13 1. The principle of displacement 13 2. Affine displacement Ln 14 3. Torsion. ... 17 4. WEYL connection . 18 5. Metrical connection 19 6. Curvature. . . 19 7. Integrability 20 8. Some identities 21 9. Non-holonomic systems 22 10. Transformation groups 23 IH. Connections associated with differential equations 24 1. Paths ... 24 2. Projective transformations 25 3. THoMAs parameters ...

Fat Manifolds and Linear Connections

... a path in a Riemannian manifold gave birth to the concept of a linear connection on M at the end of 19th century. ... In particular, it does not allow an immediate natural extension of the theory to some recently emerged situations ...

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Publisher:

ISBN: 9789814470681

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Topics in the Geometric Theory of Linear Systems

for fE F ( Z ) VE V ( z ) r ( T ( Z ) ) rer ( E ) a The basic geometric " invariant " associated with a linear connection is the curvature tensor . E over z . Definition . Let T be a linear connection for a vector bundle The curvature ...

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Author: Robert Hermann

Publisher: Math Science Press

ISBN: 091569235X

Category: Technology & Engineering

Page: 291

View: 818

Singularity Theory

Based on this last observation, we are going to introduce the notion of linear direct connection, discussed in the next section. [] 5. Direct Connections and Chern Character. A linear direct connection in the vector bundle & over the ...

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Author: Denis Ch‚niot

Publisher: World Scientific

ISBN: 9789812704108

Category: Mathematics

Page: 1065

View: 983

The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.

Encyclopaedia of Mathematics

A connection Y is called a non-linear connection of order p=1,2,..., if p is the smallest number for which the functor Y ... [5] KAWAGUCHI, A.: “On the theory of non-linear connections I. Introduction to the theory of general non-linear ...

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Author: M. Hazewinkel

Publisher: Springer

ISBN: 9781489937919

Category: Mathematics

Page: 929

View: 394

The Non Linear Field Theories of Mechanics

(ii) The functions T,”= I.”(X), determined by 6,44– T. a'd, 9 (34.4) define a linear connection Ton 2. Indeed, it is easily verified that the g., and the I.," obey the transformation laws of a covariant tensor field and of a linear ...

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Author: C. Truesdell

Publisher: Springer Science & Business Media

ISBN: 9783662103883

Category: Science

Page: 602

View: 345

This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by S. Antman who describes the monograph`s genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also has greatly contributed to the unification and standardization of the concepts, terms and notations in the field.