# Geometry, Gravity and Supersymmetry

24-28 April 2017
Mainz Institute for Theoretical Physics, Johannes Gutenberg University
Europe/Berlin timezone

## Completeness in Projective Special Geometry

24 Apr 2017, 16:30
30m
02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

### 02.430

#### Mainz Institute for Theoretical Physics, Johannes Gutenberg University

Staudingerweg 9 / 2nd floor, 55128 Mainz

### Speaker

Dr Stefan Suhr (Department of Mathematics, University of Hamburg)

### Description

One way to construct quaternionic Kähler manifolds (target spaces for sigma models in $N=2$ supersymmetric theories of gravity) is via the supergravity c-map (Ferrara-Sabharwal'90) from projective special Kähler manifolds and its combination with the supergravity r-map (deWit-Van Proeyen'92) from projective special real manifolds. After briefly introducing the structures involved I will discuss conditions for the geodesic completeness of projective special real and projective special Kähler manifolds. It is known that geodesic completeness is preserved under both the r-map and the c-map (Cortés-Han-Mohaupt'12). I will argue that projective special Kähler manifolds are complete if the condition of "regular boundary behavior" is satisfied (Cortés-Dyckmanns-Suhr'17). Projective real manifolds will be shown to be complete if they are closed as hypersurfaces in Euclidian space (Cortés-Nardmann-Suhr).

### Primary author

Dr Stefan Suhr (Department of Mathematics, University of Hamburg)

 Slides