- #1

- 42

- 10

How does this work in 3D?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter Narasoma
- Start date

In summary, the conversation discusses the concept of defining curvature on a 2D manifold using a triangle and how this applies in 3D. It is explained that in 3D, there are multiple independent components for the curvature tensor and the specific one chosen depends on the orientation of the triangle. A visual illustration of this concept is provided using an animated example from Wikipedia.

- #1

- 42

- 10

How does this work in 3D?

Physics news on Phys.org

- #2

- 20,906

- 11,873

- #3

Staff Emeritus

- 11,308

- 8,729

It is animated, so watch it for a while until you see all the vectors.

https://en.wikipedia.org/wiki/Riemann_curvature_tensor

An illustration of the motivation of Riemann curvature on a sphere-like manifold. The fact that this transport may define two different vectors at the start point gives rise to Riemann curvature tensor. The right angle symbol denotes that the inner product (given by the metric tensor) between transported vectors (or tangent vectors of the curves) is 0.

Share:

- Replies
- 8

- Views
- 334

- Replies
- 6

- Views
- 1K

- Replies
- 29

- Views
- 1K

- Replies
- 11

- Views
- 398

- Replies
- 25

- Views
- 2K

- Replies
- 5

- Views
- 828

- Replies
- 20

- Views
- 566

- Replies
- 4

- Views
- 602

- Replies
- 3

- Views
- 372

- Replies
- 7

- Views
- 305