In Chapter VIII, we learned about Pfaff forms and saw that differential forms of first degree are closely connected with the theory of line integrals. In this chapter, we will treat the higher-dimensional analogue of line integrals, in which differential forms of higher degree are integrated over certain submanifolds of ℝ n . So this chapter will deal with the theory of differential forms.
KeywordsRiemannian Manifold Volume Form Riemannian Metrics Multilinear Algebra Section VIII
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