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A linear functional on a smooth differential form.

A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. In general, these transformation properties differ from ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

To predict the result of a measurement requires (1) a model of the system under investigation, and (2) a physical theory linking the parameters of the model to the parameters ...

Differential Geometry

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

A projective module generalizes the concept of the free module. A module M over a nonzero unit ring R is projective iff it is a direct summand of a free module, i.e., of some ...

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...

A coordinate system obtained by inversion of the bicyclide coordinates. They are given by the transformation equations x = Lambda/(aUpsilon)snmudnnucospsi (1) y = ...