Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Null Sasaki eta-Einstein Structures in Five Manifolds

Jaime Cuadros

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 $η$-Einstein structures if and only if $k\in \{3,..., 21\}$. After this, we determine the moduli space of simply connected null Sasaki $η$-Einstein structures. This is accomplished using information on the moduli of lattice polarized K3 surfaces.

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 admit null Sasaki -Einstein structures if and only if . After this, we determine the moduli space of simply connected null Sasaki -Einstein structures. This is accomplished using information on the moduli of lattice polarized K3 surfaces.

Paper Structure

This paper contains 10 sections, 6 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Basics on Orbifolds.
  4. Sasaki $\eta$-Einstein Structures.
  5. Seifert Bundles and K3 Surfaces
  6. K3 Surfaces
  7. Null Sasaki $\eta$-Einstein Structures in Dimension Five
  8. Deformations of Transverse Holomorphic Sasakian Structures
  9. Deformations of Null Sasaki $\eta$-Einstein in Dimension five
  10. Tables

Key Result

Theorem 3.1

Let $({\mathcal{Z}}, \omega)$ be a Hodge orbifold. Every $[\omega]\in\mathcal{K}_L(\mathcal{Z})$ determines a Seifert $S^1$-bundle or equivalently a principal $S^1$ V-bundle $\pi: M_{[\omega]}\longrightarrow {\mathcal{Z}}$ and choosing a connection $\eta$ in $M_{[\omega]}$ whose curvature is $\pi^*\

Theorems & Definitions (12)

  • Definition 2.1
  • Definition 2.2
  • Theorem 3.1: BBG
  • Theorem 3.2
  • Lemma 3.3
  • Definition 3.4
  • Theorem 3.5: Ko
  • Remark 3.1
  • Corollary 3.6
  • Lemma 4.1
  • ...and 2 more