Generalized pentagonal geometries

Courant-Nijenhuis tensors and generalized geometries

Nijenhuis tensors N on Courant algebroids compatible with the pairing are studied. This compatibility condition turns out to be of the form N + N = λI for irreducible Courant algebroids, in particular for the extended tangent bundles T M = TM ⊕ TM . It is proved that compatible Nijenhuis tensors on irreducible Courant algebroids must satisfy quadratic relations N −λN + γI = 0, so that the corre...

AdS Vacua, Attractor Mechanism and Generalized Geometries

We consider flux vacua attractor equations in type IIA string theory compactified on generalized geometries with orientifold projections. The four-dimensional N = 1 superpotential in this compactification can be written as the sum of the Ramond-Ramond superpotential and a term described by (non)geometric flux charges. We exhibit a simple model in which supersymmetric AdS and Minkowski solutions...

Projective Representations II. Generalized chain geometries

In this paper, projective representations of generalized chain geometries are investigated, using the concepts and results of [5]. In particular, we study under which conditions such a projective representation maps the chains of a generalized chain geometry Σ(F,R) to reguli; this mainly depends on how the field F is embedded in the ring R. Moreover, we determine all bijective morphisms of a ce...

Projective Representations II. Generalized chain geometries

Waverider Design for Generalized Shock Geometries

A new method for the design of waverider con-gurations with generalized shock geometries is presented. An arbitrary three-dimensional shock shape is speciied as input, and a cross-stream Euler marching procedure is used to deene the post-shock ow-eld. Unlike most previous studies, this approach allows for the use of nonaxisymmetric shock topologies with nonconstant shock strengths. The problem'...