An Inequality for Betti Numbers of Hyper-Kaehler Manifolds of Dimension 6

摘要

A hyper-Kaehler manifold is a Riemannian manifold M with a triple of complex structures I, J, and K satisfying the following conditions: (ⅰ) the metric g on M is Kaehler for these complex structures; (ⅱ) any endomorphisms I, J, and K of the real tangent bundle satisfy the following two relations I o J = - J o I = K and I~2 = J~2 = K~2 = -1.