1.Previous
3.Next

tangent space based solely on the manifold itself.

There are various equivalent ways of defining the tangent spaces of a manifold. While the definition via the velocity of curves is intuitively the simplest, it is also the most cumbersome to work with. More elegant and abstract approaches are described below.

Definition via tangent curves

In the embedded-manifold picture, a tangent vector at a point is thought of as the velocity of a curve passing through the point . We can therefore

1.Previous
3.Next