Null Sasaki eta-Einstein Structures in Five Manifolds

Abstract

We study null Sasakian structures in dimension five. First, based on a result due to Kollár [Ko], we improve a result by Boyer, Galicki and Matzeu in [BGM] and prove that simply connected manifolds diffeomorphic to $# k(S^2\times S^3)$ admit null Sasaki $\eta$-Einstein structures if and only if $k\in \{3,...,21\}$. After this, we determine the moduli space of simply connected null Sasaki $\eta$-Einstein structures. This is accomplished using information on the moduli of lattice polarized K3 surfaces.

References in corpus (2)

• Limits of Calabi-Yau metrics when the Kahler class degenerates
• Lorentzian Sasaki-Einstein Metrics on Connected Sums of $S^2\times S^3$

Cited by in corpus (1)

• Sasaki-Einstein 7-manifolds and Orlik's conjecture