Calabi–Yau manifold

High school (ages 12+)
Space & Astronomy

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Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/calabiyau-manifold

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the conjectured by?Eugenio Calabi (1954, 1957)
2. What is the conjecture proven by?Shing-Tung Yau (1978)
3. Why do scientists use Calabi–Yau manifolds in string theory?In string theory the universe has extra tiny dimensions that are curled up. Calabi–Yau manifolds are good shapes for these curled dimensions because their geometry lets the strings vibrate in ways that match the particles we see.
4. How many dimensions does a Calabi–Yau manifold have?They can have many even numbers of real dimensions, but the most studied ones have six dimensions.

Ricci-flat Metric: A Riemannian metric on a manifold whose Ricci curvature tensor vanishes identically.
Kähler Manifold: A complex manifold equipped with a compatible Riemannian metric and symplectic form.
Compactification: The process in string theory where extra spatial dimensions are curled up into small geometric spaces.
Mirror Symmetry: A duality between pairs of Calabi-Yau manifolds that leads to identical physical theories.