Geometry of Differential Forms Shigeyuki Morita
Publisher: American Mathematical Society

It's also important to remember that differential forms don't have to be real-valued. Definitions of curvature, curvature tensor; Second fundamental form; Sectional and Ricci curvature; Jacobi fields. I have concrete questions about it and it would be very nice, when someone. Hello, i have a proof of a statement, but i don't understand it very well. Integrals of differential forms play a fundamental role in modern differential geometry. I see: Maybe I should be more careful when I talk about “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: $$S_{eff} sim S^{(0)} + alpha S^{(1)} + (alpha)^2 S^{(2)} + ldots$$. Principal theorems and applications of differential. In classical differential geometry, given a real, smooth maifold M , the differential df of a real smooth function f lives in the cotangential bundle of M . Most readers will know that one can impose a Differentiable Structure on a topological manifold and use it to start doing some geometry. The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. CARTAN'S LEMMAS ON DIFFERENTIAL FORMS.