Geometry of Differential Forms Shigeyuki Morita
Publisher: American Mathematical Society

Let us try to write the four Maxwell equations using the language of differential forms, exterior differentiation and the Hodge star duality operation. This is considered in higher symplectic geometry, specifically: in multisymplectic geometry. So geometry killed the electric and magnetic fields. 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. Do Carmo Differential Forms and Applications "This book treats differential forms and uses them to study some local and global aspects of differential geometry of surfaces. This applications demonstrates some of the new functionality in Maple 16 for working with abstractly defined differential forms, general relativity, and Lie algebras. He indeed showed how all other efforts in geometry fit into his scheme. The notion of n -plectic form is a generalization of the notion of symplectic form to differential forms of more than two arguments. In addition to collecting results on the geometry of singularities and classification of differential forms and Pfaffian equations, this monograph discusses applications and closely related classification problems. In the process, he gave the differential form of Euclid's postulates in spaces of any number of dimensions.