Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

- Index
- » Science HQ
- »
**Geodesics**

Pages: **1**

**Jaspers****Member**- Registered: 2019-05-24
- Posts: 52

A geodesic on a smooth manifold *M* with an affine connection ∇ is defined as a curve *γ*(*t*) such that parallel transport along the curve preserves the tangent vector to the curve, i.e.

at each point along the curve, where

is the derivative with respect to *t*.

Using local coordinates on *M*, we can write the geodesic equation (using the summation convention) as the ordinary differential equation

where

are the coordinates of the curve *γ*(*t*) and

are the Christoffel symbols of the connection ∇.

[Source: Wikipedia]

Reason is like an open secret that can become known to anyone at any time; it is the quiet space into which everyone can enter through his own thought.

Offline

Pages: **1**

- Index
- » Science HQ
- »
**Geodesics**