Berger's inequality for Einstein manifolds

Short description: Any 4-dimensional Einstein manifold has a non-negative Euler characteristic

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 France mathematician Marcel Berger.

See also

• Hitchin–Thorpe inequality

References

• Besse, Arthur L. (1987). Einstein Manifolds. Classics in Mathematics. Berlin: Springer. ISBN 3-540-74120-8. https://archive.org/details/einsteinmanifold0000bess.