Volume Forms

  • Serge Lang
Part of the Graduate Texts in Mathematics book series (GTM, volume 160)


For the first time we meet a strictly finite dimensional phenomenon: If X is of finite dimension n, then the n-forms An(X) play a distinguished role whose extension to the infinite dimensional case is not evident. So this chapter is devoted to these forms of maximal degree. In the next chapter, we shall study how to integrate them, so the present chapter also provides a transition from the differential theory to the integration theory.


Vector Field Riemannian Manifold Orthonormal Basis Covariant Derivative Orthonormal Frame 
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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

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

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