Pullback (differential geometry): Differential Form, Tensor, Differentiable Manifold, Pullback, Smooth Function, Linear Map, Section, Cotangent Bundle - Couverture souple

 
9786130343859: Pullback (differential geometry): Differential Form, Tensor, Differentiable Manifold, Pullback, Smooth Function, Linear Map, Section, Cotangent Bundle
Couverture souple
ISBN 10 : 613034385X ISBN 13 : 9786130343859
Editeur : Betascript Publishing, 2010

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Suppose that φ:M→ N is a smooth map between smooth manifolds M and N; then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by φ), and is frequently denoted by φ*. More generally, any covariant tensor field – in particular any differential form – on N may be pulled back to M using φ. When the map φ is a diffeomorphism, then the pullback, together with the pushforward, can be used to transform any tensor field from N to M or vice-versa. In particular, if φ is a diffeomorphism between open subsets of Rn and Rn, viewed as a change of coordinates (perhaps between different charts on a manifold M), then the pullback and pushforward describe the transformation properties of covariant and contravariant tensors used in more traditional (coordinate dependent) approaches to the subject.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Suppose that φ:M→ N is a smooth map between smooth manifolds M and N; then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by φ), and is frequently denoted by φ*. More generally, any covariant tensor field – in particular any differential form – on N may be pulled back to M using φ. When the map φ is a diffeomorphism, then the pullback, together with the pushforward, can be used to transform any tensor field from N to M or vice-versa. In particular, if φ is a diffeomorphism between open subsets of Rn and Rn, viewed as a change of coordinates (perhaps between different charts on a manifold M), then the pullback and pushforward describe the transformation properties of covariant and contravariant tensors used in more traditional (coordinate dependent) approaches to the subject.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Betascript Publishing
Date d'édition
2010
Langue
anglais
ISBN 10 
613034385X
ISBN 13 
9786130343859
Reliure
Broché
Nombre de pages
80
Éditeur
Surhone Lambert M., Tennoe Mariam T., Henssonow Susan F.
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9786130343712: Pullback (category theory): Category Theory, Mathematics, Limit, Diagram, Morphism, Span, Commutative Diagram

Edition présentée

ISBN 10 :  613034371X ISBN 13 :  9786130343712
Editeur : Betascript Publishing, 2010
Couverture souple