---- > [!definition] Definition. ([[metric tensor]]) > Let $M$ be a [[smooth manifold]]. A **metric tensor (field)**, or simply **metric**, on $M$ is smooth section of $\mathbb{S}^{2} T^{*}M$, the second [[symmetric power]] [[tensor product of vector bundles|of the]] [[cotangent bundle]], that is [[nondegenerate bilinear form|nondegenerate]] at each point. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```