# Berger's inequality for Einstein manifolds

In mathematics — specifically, in differential topology — **Berger's inequality for Einstein manifolds** is the statement that any 4-dimensional Einstein manifold (*M*, *g*) has non-negative Euler characteristic *χ*(*M*) ≥ 0. The inequality is named after the French mathematician Marcel Berger.

## See alsoEdit

## ReferencesEdit

- Besse, Arthur L. (1987).
*Einstein Manifolds*. Classics in Mathematics. Berlin: Springer. ISBN 3-540-74120-8.

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