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In linear algebra, a one-form on a vector space is the same as a linear functional on the space. The usage of ''one-form'' in this context usually distinguishes the one-forms from higher-degree multilinear functionals on the space. For details, see linear functional. In differential geometry, a one-form on a differentiable manifold is a smooth section of the cotangent bundle. Equivalently, a one-form on a manifold ''M'' is a smooth mapping of the total space of the tangent bundle of ''M'' to whose restriction to each fibre is a linear functional on the tangent space. Symbolically, : where αx is linear. Often one-forms are described locally, particularly in local coordinates. In a local coordinate system, a one-form is a linear combination of the differentials of the coordinates: : where the ''f''''i'' are smooth functions. From this perspective, a one-form has a covariant transformation law on passing from one coordinate system to another. Thus a one-form is an order 1 covariant tensor field. ==Examples== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「One-form」の詳細全文を読む スポンサード リンク
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