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.
KeywordsVector Field Riemannian Manifold Orthonormal Basis Covariant Derivative Orthonormal Frame
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