Fat manifolds and linear connections /
De Paris, Alessandro.
Fat manifolds and linear connections / Alessandro De Paris, Alexandre Vinogradov. - Hackensack, NJ : World Scientific, ©2009. - 1 online resource (xii, 297 pages) : illustrations
Includes bibliographical references (pages 281-282) and index.
Elements of differential calculus over commutative algebras -- Basic differential calculus on fat manifolds -- Linear connections -- Covariant differential -- Cohomological aspects of linear connections.
In this unique book, written in a reasonably self-contained manner, the theory of linear connections is systematically presented as a natural part of differential calculus over commutative algebras. This not only makes easy and natural numerous generalizations of the classical theory and reveals various new aspects of it, but also shows in a clear and transparent manner the intrinsic structure of the associated differential calculus. The notion of a "fat manifold" introduced here then allows the reader to build a well-working analogy of this "connection calculus" with the usual one.
9789812819055 (electronic bk.) 9812819053 (electronic bk.)
2009277313
Differential calculus.
Commutative algebra.
Manifolds (Mathematics)
Algebras, Linear.
Calcul différentiel.
Algèbre commutative.
Variétés (Mathématiques)
Algèbre linéaire.
MATHEMATICS--Differential Equations--General.
Algebras, Linear.
Commutative algebra.
Differential calculus.
Manifolds (Mathematics)
Electronic books.
Electronic books.
QA304 / .D47 2009eb
515/.33
Fat manifolds and linear connections / Alessandro De Paris, Alexandre Vinogradov. - Hackensack, NJ : World Scientific, ©2009. - 1 online resource (xii, 297 pages) : illustrations
Includes bibliographical references (pages 281-282) and index.
Elements of differential calculus over commutative algebras -- Basic differential calculus on fat manifolds -- Linear connections -- Covariant differential -- Cohomological aspects of linear connections.
In this unique book, written in a reasonably self-contained manner, the theory of linear connections is systematically presented as a natural part of differential calculus over commutative algebras. This not only makes easy and natural numerous generalizations of the classical theory and reveals various new aspects of it, but also shows in a clear and transparent manner the intrinsic structure of the associated differential calculus. The notion of a "fat manifold" introduced here then allows the reader to build a well-working analogy of this "connection calculus" with the usual one.
9789812819055 (electronic bk.) 9812819053 (electronic bk.)
2009277313
Differential calculus.
Commutative algebra.
Manifolds (Mathematics)
Algebras, Linear.
Calcul différentiel.
Algèbre commutative.
Variétés (Mathématiques)
Algèbre linéaire.
MATHEMATICS--Differential Equations--General.
Algebras, Linear.
Commutative algebra.
Differential calculus.
Manifolds (Mathematics)
Electronic books.
Electronic books.
QA304 / .D47 2009eb
515/.33