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Metric (vector bundle)
In differential geometry, the notion of a metric tensor can be extended to an arbitrary vector bundle. Specifically, if ''M'' is a topological manifold and ''E'' → ''M'' a vector bundle on ''M'', then a metric (sometimes called a bundle metric, or fibre metric) on ''E'' is a bundle map ''g'' : ''E'' ×''M'' ''E'' → ''M'' × R from the fiber product of ''E'' with itself to the trivial bundle with fiber R such that the restriction of ''g'' to each fibre over ''M'' is a nondegenerate bilinear map of vector spaces.〔.〕
==References==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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