Tensor Fields and Differential Forms

Abstract

AbstractAfter providing some definitions and results on tensor fields and differential forms, this chapter deals with some aspects of general vector bundles, including the ‘cocycle approach’; other topics are: Tensors and tensor fields, exterior forms, Lie derivative and the interior product; calculus of differential forms and distributions. Some examples related to manifolds studied in the previous chapter are also present, such as the infinite Möbius strip, considered as a vector bundle, and the tautological bundle over the real Grassmannian. Certain problems intend to make the reader familiar with computations of vector fields, differential forms, Lie derivative, the interior product, the exterior differential, and their relationships. Other group of problems tries to develop practical abilities in computing integral distributions and differential ideals.KeywordsVector FieldVector BundleDifferential FormKind PermissionDifferential IdealThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.