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Geometry of Differential Forms Shigeyuki Morita
Publisher: American Mathematical Society

I need the applications of differential geometry to image analysis and processing, and in the connections to calculus of variations, PDE and numerical analysis. The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. Constructions in synthetic differential geometry. Finally, I'd like to read books/papers like “Geometric Partial Differential . Flanders would be a good book to start with as he does not assume much background. Examples of 2-connections with vanishing 2-form curvature obtained from geometric quantization are discusssed in. Contents look very promising: begins directly with manifold definition, proceed with structures, include PDE, tensors, differential forms, Lie groups, and topology. It took me quite a while to find a good explanation of differential forms & I Spivak has a nice quip in Differential Geometry, Vol. Olivier Brahic, On the infinitesimal Gauge Symmetries of closed forms (arXiv). "Differential Forms with Applications to the Physical Sciences" by H. Recall from the discussion there what such form data looks like. Tangent bundle; Differential equation; Differential forms. Idea; Axiomatics; Models; Well adapted models; Variations. This has given me the chance to apply differential-geometric techniques to problems which I used to believe could only be approached analytically. Introduction to Differential Geometry,” 3rd ed., Publish or Perish, 1999. Let 𝔤 be some Lie 2-algebra. In Calculus is being discussed at Physics Forums. When the underlying principal 2-bundle over a smooth manifold X is topologically trivial, then the connections on it are identified with Lie 2-algebra valued differential forms on X . Higher categorical versions; Supergeometric versions.