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Geometry of Differential Forms Shigeyuki Morita
Publisher: American Mathematical Society

Integrals of differential forms play a fundamental role in modern differential geometry. This definitely is a text for physicists, not mathematicians, with the geometry taking a back-seat. I'm currently working through a differential geometry book that uses Clifford's algebra instead of differential forms. DG - Clifford Algebra / Differential Forms in Differential Geometry is being discussed at Physics Forums. Tangent bundle; Differential equation; Differential forms. Caltech | Fall 2012 Ultimately we'll interpret the symbol \(\wedge\) (pronounced “wedge”) as a binary operation on differential forms called the wedge product. Constructions in synthetic differential geometry. We are going to call this a "differential 1-form", but we would do well to notice the things that our text is not telling us - first that this construction implies we are working over a 3-manifold (Euclidean flat, sure enough), and moreover that is a vector in the co-tangent space to this manifold. Higher categorical versions; Supergeometric versions. CS 177: Discrete Differential Geometry. This textbook introduces geometric measure theory through the notion of currents. This is a pity because SDG allows you to do an amazing thing - write computer programs that easily manipulate objects such as vector fields and differential forms on manifolds without doing symbolic algebra. Differential forms and orthonormal frames don't appear until nearly the end of the book. 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: $$S_{eff} \sim S^{(0)} + \alpha S^{(1)} + (\alpha)^2 S^{(2)} + \ldots$$. CARTAN'S LEMMAS ON DIFFERENTIAL FORMS. Principal theorems and applications of differential. This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The naive view of a tangent will have it "sticking out" into some surrounding (one says embedding) space, and this we cannot allow - we want to do intrinsic geometry. Idea; Axiomatics; Models; Well adapted models; Variations. We'd like to use this form as our top form, but it's heavily dependent on our choice of coordinates, so it's very much not a geometric object — our ideal choice of a volume form will be independent of particular coordinates.