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Geometry of Differential Forms Shigeyuki Morita
Publisher: American Mathematical Society

CS 177: Discrete Differential Geometry. An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. This text presents differential forms from a geometric perspective accessible at the undergraduate level. Almost any differential geometry entity can be indexed - any object (constant, tensor, p-form, manifold etc.) can be indexed. This has given me the chance to apply differential-geometric techniques to problems which I used to believe could only be approached analytically. For or more information on atlas indexing facilities, see atlas[indexing]. I've been studying differential. I have a doubt about the physical and geometrical interpretation of differential forms. In the context of string theory, in particular when we're dealing with a low energy effective action, if we have an effective action of the form: $$S_{eff} \sim S^{(0)} + \alpha S^{(1)} + (\alpha)^2 S^{(2)} + \ldots$$. This textbook introduces geometric measure theory through the notion of currents. Caltech | Fall 2012 Ultimately we'll interpret the symbol \(\wedge\) (pronounced “wedge”) as a binary operation on differential forms called the wedge product. Euclidean geometry was abandoned in favour of di erential geometry and classical eld theories had to be quantized. Differential forms are introduced in a simple way that will make them attractive to “users” of mathematics.