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

 
9786130343859: Pullback (differential geometry): Differential Form, Tensor, Differentiable Manifold, Pullback, Smooth Function, Linear Map, Section, Cotangent Bundle
Softcover
ISBN 10: 613034385X ISBN 13: 9786130343859
Verlag: Betascript Publishers, 2010

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Betascript Publishers
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
613034385X
ISBN 13 
9786130343859
Einband
Tapa blanda
Anzahl der Seiten
80
Herausgeber
Surhone Lambert M., Tennoe Mariam T., Henssonow Susan F.
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

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

Vorgestellte Ausgabe

ISBN 10:  613034371X ISBN 13:  9786130343712
Verlag: Betascript Publishers, 2010
Softcover