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In mathematics, the interior product or interior derivative is a degree −1 antiderivation on the exterior algebra of differential forms on a smooth manifold. The interior product, named in opposition to the exterior product, is also called interior or inner multiplication, or the inner derivative or derivation, but should not be confused with an inner product. The interior product ''ι''''X''''ω'' is sometimes written as ''X'' (unicode:⨼) ''ω''.〔The character (unicode:⨼) is U+2A3C in Unicode〕 ==Definition== The interior product is defined to be the contraction of a differential form with a vector field. Thus if ''X'' is a vector field on the manifold ''M'', then : is the map which sends a ''p''-form ''ω'' to the (''p''−1)-form ''ι''''X''''ω'' defined by the property that : for any vector fields ''X''1, ..., ''X''''p''−1. The interior product is the unique antiderivation of degree −1 on the exterior algebra such that on one-forms ''α'' :, the duality pairing between ''α'' and the vector ''X''. Explicitly, if ''β'' is a ''p''-form and γ is a ''q''-form, then : The above relation says that the interior product obeys a graded Leibniz rule. An operation equipped with linearity and a Leibniz rule is often called a derivative. 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「interior product」の詳細全文を読む スポンサード リンク
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