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

Lambert M. Surhone (u. a.)

ISBN 10: 613034385X / ISBN 13: 9786130343859

Published by OmniScriptum, 2026

About this Item

Pullback (differential geometry) | Differential Form, Tensor, Differentiable Manifold, Pullback, Smooth Function, Linear Map, Section, Cotangent Bundle | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130343859 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.

Seller Inventory # 101372937

Bibliographic Details

• Title: Pullback (differential geometry) | Differential Form, Tensor, Differentiable Manifold, Pullback, Smooth Function, Linear Map, Section, Cotangent Bundle
• Publisher: OmniScriptum
• Publication Date: 2026
• Language: English
• ISBN 10: 613034385X
• ISBN 13: 9786130343859
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 5D millimeters 220 millimeters width by 150 millimeters height by 5 millimeters depth
• Weight: 137 grams
• Seller catalogs:
  • Bücher

About this title

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.