affine connection in Vietnamese

@Chuyên ngành kỹ thuật
-liên thông affin
-liên thông afi

Sentence patterns related to "affine connection"

1. Conversely if ∇ is an affine connection and Γ is such a smooth bilinear bundle homomorphism (called a connection form on M) then ∇ + Γ is an affine connection.

2. Curvature and torsion are the main invariants of an affine connection.

3. The main invariants of an affine connection are its torsion and its curvature.

4. The notion of an affine connection was introduced to remedy this problem by connecting nearby tangent spaces.

5. In this language, an affine connection is simply a covariant derivative or (linear) connection on the tangent bundle.

6. In formal terms, let τ0 t : TxtM → Tx0M be the linear parallel transport map associated to the affine connection.

7. If M is a surface in R3, it is easy to see that M has a natural affine connection.

8. The complex history has led to the development of widely varying approaches to and generalizations of the affine connection concept.

9. An affine connection is called complete if the exponential map is well-defined at every point of the tangent bundle.

10. This yields a possible definition of an affine connection as a covariant derivative or (linear) connection on the tangent bundle.

11. This follows from the Picard–Lindelöf theorem, and allows for the definition of an exponential map associated to the affine connection.

12. A basic result of differential geometry states that normal coordinates at a point always exist on a manifold with a symmetric affine connection.

13. The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully developed until the early 1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part of his foundations for general relativity).