Chapter V

Exterior Differential Forms


Exterior differential forms; Exterior algebra; Interior product; Top-down generated bases; Ideals of exterior algebra; Characteristic vectors; Pull-back operator; Exterior derivative; Riemannian manifolds; Hodge dual; Co-differential; Laplace-de Rham operator; Laplace-Beltrami operator; Closed ideals; Lie derivative of forms; Isovecor fields; Exterior systems; Complete integrability; Frobenius' theorem; Forms defined on a Lie group; Maurer-Cartan forms

5.1 Scope of the Chapter

Studies of differential forms has started with the works of Grassmann and efforts to extend the integral theorems in classical vector analysis has played a significant part in the development of the theory. Several elemental concepts, ...

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