Null Sasaki eta-Einstein Structures in Five Manifolds

Details Null Sasaki eta-Einstein Structures in Five Manifolds Null Sasaki eta-Einstein Structures in Five Manifolds

2009-09-25

arxiv.org/abs/0909.4581v1

Mathematics

Differential Geometry

Scientific paper

We study null Sasakian structures in dimension five. First, based on a result due to Koll\'ar [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.

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