Operations on Vector Fields and Differential Forms

  • Serge Lang
Part of the Graduate Texts in Mathematics book series (GTM, volume 191)


If EX is a vector bundle, then it is of considerable interest to investigate the special operation derived from the functor “multilinear alternating forms.” Applying it to the tangent bundle, we call the sections of our new bundle differential forms. One can define formally certain relations between functions, vector fields, and differential forms which lie at the foundations of differential and Riemannian geometry. We shall give the basic system surrounding such forms. In order to have at least one application, we discuss the fundamental 2-form, and in the next chapter connect it with Riemannian metrics in order to construct canonically the spray associated with such a metric.


Vector Field Vector Bundle Differential Form Tangent Bundle Local Representation 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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