We classify nilmanifolds with an invariant symplectic half-flat structure. We solve the half-flat evolution equations in one example, writing down the resulting Ricci-flat metric. We study the geometry of the orbit space of 6-manifolds with an SU(3)-structure preserved by a U(1) action, giving characterizations in the symplectic half-flat and integrable case.

The design and construction of non-flat interactive surfaces is an emerging field of research. In this paper, we propose a design space for such displays in order to support structured discussions about differences and design possibilities within this area. Our design space is spanned by basic dimensions of shaped display surfaces, such as size, form and texture. As a starting point, we classif...

Introduction. The Knizhnik-Zamolodchikov-Bernard connection ([22, 5, 27]) can be viewed as a flat connection over the complement det∗g,ν of the zero-section in the total space of the determinant line bundle over the moduli space Mg,ν·12 of genus g curves with ν marked points and tangent vectors ([4]). Projectivization of this connection is the pull-back of a flat projective connection on Mg,ν·1...

We know that there is an isomorphism between the moduli space of gauge equivalence classes of flat G-connections on a compact surface and the moduli space of representations from the fundamental group of the surface to G acted on by the adjoint action (cf: Goldman[G]). It is known that if G is compact, semi-simple and simply connected, the moduli space of gauge equivalence classes of flat G-con...

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl’s construction is generalized here to arbitrary dimension D ≥ 4. The general solution of the D-dimensional vacuum Einstein equations that admits D− 2 orthogonal com...

Let X = Γ\G/K be a compact locally symmetric space. In this paper we establish a version of the Selberg trace formula for non-unitary representations of the lattice Γ. On the spectral side appears the spectrum of the “flat Laplacian” ∆, acting in the space of sections of the associated flat bundle. In general, this is a non-self-adjoint operator.