- #1

MathematicalPhysicist

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what are they?

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- Thread starter MathematicalPhysicist
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- #1

MathematicalPhysicist

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what are they?

- #2

selfAdjoint

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1) They are Kaehler manifolds. As manifolds they have a Riemannian metric, and as complex spaces they have a Hermitian form, and in Kaehler manifolds these two conditions are compatible. I can't get any more specific than that without giving a course in Kaehler manifolds.

2) They satisfy a topological constraint called the vanishing of the first Chern class. This means that they are pretty smooth.

Calabi conjectured that in manifolds like this the Ricci curvature (from Riemannian geometry) would vanish. They would be "locally flat" in a technical sense.

Yau proved Calabi's conjecture and constructed the family of Calabi-Yau manifolds that string theorists use today.

- #3

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Where to begin to learn such things?

Can you recommend some self contained books about subject.

Can you recommend some self contained books about subject.

- #4

phyzguy

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