---- > [!definition] Definition. ([[tangent vector to a regular surface]]) > A **tangent vector** to a [[differentiable Euclidean submanifold|regular surface]] (more generally, a differentiable embedded Euclidean submanifold) at a point $p$ is a [[vector]] which is the [[velocity vector of a parameterized curve|velocity (tangent) vector]] $\gamma'(0)$ of a differentiable [[parameterized curve|parameterized curve]] $\gamma:(-\varepsilon, \varepsilon) \to S$ with $\alpha(0)=p$. > [!generalization] > [[tangent vector to a smooth manifold]] ^generalization ---- #### ---- #### 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 > ```