Supersymmetric Geometries in Type IIA Supergravity

Abstract: This thesis is about supersymmetric geometries in type IIA supergravity and their classification using spinorial geometry. Appended is our first paper on the topic. There are four types of Killing spinors to treat, distinguished by their isotropy group. The appended paper treats the cases where the isotropy group is Spin(7) or Spin(7) ⋉ ℝ⁸. The first part of the thesis introduces the method and some important concepts that should help the reader understand the paper. After an introduction describing supersymmetry and supergravity, we turn to spinors and the Spin(p, q) groups, and proceed to the Killing spinor equations and the method of spinorial geometry. The method results in a linear system of equations (the exact expression is appended the paper), and in chapter 4 the reader is shown how to go about in simplifying it to arrive at the final expressions found in the paper.