The seven and nine dimensional geometries associated with certain classes of supersymmetric AdS3 and AdS2 solutions of type IIB and D = 11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further elucidate their properties and also generalise them to higher odd dimensions by introducing a new class of complex geometries in 2n+2 dimensions, specified by a Riem...

We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles nonspheroidal, nonaxisymmetric objects, and objects with sharp corners. Using our new technique, we obtain the first predictions of Casimir interactions in a number of experimentally rele...

Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous.