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Tensors

  • Ralph Abraham
  • Jerrold E. Marsden
  • Tudor Ratiu
Part of the Applied Mathematical Sciences book series (AMS, volume 75)

Abstract

In the previous chapter we studied vector fields and functions on manifolds. Now these objects are generalized to tensor fields, which are sections of vector bundles built out of the tangent bundle. This study is continued in the next chapter when we discuss differential forms, which are tensors with special symmetry properties. One of the objectives of this chapter is to extend the pull-back and Lie derivative operations from functions and vector fields to tensor fields.

Keywords

Vector Field Vector Bundle Tensor Field Separable Banach Space Kill Vector Field 
These 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.

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Ralph Abraham
    • 1
  • Jerrold E. Marsden
    • 2
  • Tudor Ratiu
    • 1
  1. 1.Department of MathematicsUniversity of California—Santa CruzSanta CruzUSA
  2. 2.Control and Dynamical Systems, 107–81California Institute of TechnologyPasadenaUSA

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