Geometry of Differential Forms by Shigeyuki Morita

Geometry of Differential Forms Shigeyuki Morita ebook
Format: djvu
Page: 171
ISBN: 0821810456, 9780821810453
Publisher: American Mathematical Society

Stoker's Differential Geometry. Definitions of curvature, curvature tensor; Second fundamental form; Sectional and Ricci curvature; Jacobi fields. This has given me the chance to apply differential-geometric techniques to problems which I used to believe could only be approached analytically. This applications demonstrates some of the new functionality in Maple 16 for working with abstractly defined differential forms, general relativity, and Lie algebras. The next text up for review is J.J. Differential forms and orthonormal frames don't appear until nearly the end of the book. So I'm a little stuck on the concept of forms on a manifold. I understand what forms are, and understand their properties in R2 and R3 (exactn. 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 . I see: Maybe I should be more careful when I talk about “differential forms”. The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. Applying Algebraic Topology , Geometry and Differential Geometry in nonabelian gauge in High Energy, Nuclear, Particle Physics is being discussed at Physics Forums. 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. Any recommendations for a textbook that apply these ideas to gauge theory ? (These titles are going to of Manifolds. This definitely is a text for physicists, not mathematicians, with the geometry taking a back-seat. I 've been reading about Homotopy , homology and abstract lie groups and diff.forms and I would like to see those beautiful ideas applied on a Nonabelian Gauge Theory .