We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Beside a study of the general properties of such a cohomology, we show that, given a complex vector bundle, one can compute its topological Chern classes using the extendable Chern classes, defined via a Chern-Weil type theory. We also prove that the localizatio...

In this paper, we study differential forms and vector fields on the orbit space of a proper action Lie group smooth manifold, defining them as multilinear maps generators infinitesimal diffeomorphisms, respectively. This yields an intrinsic view space.

The calculus of differential forms has significant advantages over traditional methods as a tool for teaching electromagnetic (EM) field theory: First, forms clarify the relationship between field intensity and flux density, by providing distinct mathematical and graphical representations for the two types of fields. Second, Ampere’s and Faraday’s laws obtain graphical representations that are ...

Abstract We prove that on a closed 3-manifold of constant positive curvature the unit vector fields minimum volume are exactly Hopf fields.