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In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle. [1] Equivalently, a one-form on a manifold is a smooth mapping of the total space of the tangent bundle of to whose restriction to each fibre is a linear functional on the ...
A general 1-form is a linear combination of these differentials at every point on the manifold: + +, where the f k = f k (x 1, ... , x n) are functions of all the coordinates. A differential 1-form is integrated along an oriented curve as a line integral.
Mathematics, Form and Function, a book published in 1986 by Springer-Verlag, is a survey of the whole of mathematics, including its origins and deep structure, by the American mathematician Saunders Mac Lane.
In mathematics, a linear form (also known as a linear functional, [1] a one-form, or a covector) is a linear map [nb 1] from a vector space to its field of scalars (often, the real numbers or the complex numbers).
The apparent plural form in English goes back to the Latin neuter plural mathematica , based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of ...
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Download as PDF; Printable version; ... In mathematics, a modular form is a holomorphic function on the complex upper half-plane, ... a modular form of weight 1/2, ...
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