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Differentiable Manifolds with an Area Measure

Published online by Cambridge University Press:  20 November 2018

F. Brickell
F. Brickell*
Affiliation:
Northwestern University, Evanston, Illinois and Southampton University, Southampton, England
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In this section we fix some notations and give a definition of an area measure on a differentiate manifold, where throughout the paper the word differentiable implies differentiability of class C∞. Let M denote a differentiate manifold of dimension n and call a set of m linearly independent vectors {e1, … , em} at a point of M an m-frame of M. The set E′ of all such m-frames can be given the structure of a differentiable fibre bundle over M and we denote the projection of E' onto M by π′.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 540 - 549
Copyright
Copyright © Canadian Mathematical Society 1967

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