Differential Forms

The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the advanced undergraduate level. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually.

Learn differential forms, wedge products, exterior derivatives, the Generalized Theorem of Calculus, Hodge dual, etc.

Exploring the Quanta of Space, Differential Forms, the Tetrad formalism of GR, Canonical Relativity, Ashtekar Variables.

This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1).

Since the times of Gauss, Riemann, and Poincaré, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties.