Rigid Supersymmetry on 5-dimensional Riemannian Manifolds and Contact Geometry

Understand

In this note we generalize the methods of [1][2][3] to 5-dimensional Riemannian manifolds M.

• We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional supergravity.
• The existence of 1 pair of solutions is related to almost contact metric structures.
• We also discuss special cases related to $M = S1 \times M4$, which leads to M being foliated by submanifolds with special properties, such as Quaternion-Kahler.