# String Theory Seminar

### 13/01/2014, 16:30 — 17:30 — Room P3.10, Mathematics Building

Thomas Mohaupt, *University of Liverpool*

### (Para-)Quaternion Kähler geometry from Supergravity (Part 1)

We review some recent results on quaternion-Kähler geometry
which were obtained in the context supergravity and string
theory.

- By proving that the supergravity \(r\)-map and \(c\)-map
preserve geodesic completeness, we established a method to
construct non-homogeneous geodesically complete quaternion-Kähler
manifolds starting from complete special Kähler or special real
manifolds.
- Deriving the hyper-Kähler/quaternion-Kähler correspondence
using
*conification*, we have obtained a new proof that
spaces in the image of the \(c\)-map are quaternion-Kähler, which
extends to include the *one-loop quantum deformation*.
- Time permitting we will also discuss how some of the results
can be adapted to para-quaternion-Kähler manifolds.