Related papers: Even Dimensional Improper Affine Spheres

We consider smoothings of a complex surface with singularities of class T and no nontrivial holomorphic vector field. Under an hypothesis of non degeneracy of the smoothing at each singular point, we prove that if the singular surface…

We show how affine and projective special K\"ahler manifolds emerge from the structure of quantization. We quantize them and construct natural (wavefunction) representations for the corresponding coherent states. These in turn are shown to…

Conformal Galilei Algebras labeled by $d,\ell$ (where $d$ is the number of space dimensions and $\ell$ denotes a spin-${\ell}$ representation w.r.t. the $\mathfrak{sl}(2)$ subalgebra) admit two types of central extensions, the ordinary one…

We establish restrictions on Lagrangian embeddings of rational homology spheres into certain open symplectic manifolds, namely the (A_m) Milnor fibres of odd complex dimension. This relies on general considerations about equivariant objects…

We give some classifications of biharmonic hypersurfaces with constant scalar curvature. These include biharmonic Einstein hypersurfaces in space forms, compact biharmonic hypersurfaces with constant scalar curvature in a sphere, and some…

An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to compute the dimension of the deformation…

We introduce the notion of affine Legendrian submanifolds in Sasakian manifolds and define a canonical volume called the $\phi$-volume as odd dimensional analogues of affine Lagrangian (totally real or purely real) geometry. Then we derive…

We construct two non isomorphic contractible affine threefolds X and Y with isomorphic cylinders, showing that the generalized Cancellation Problem has a negative answer in general for contractible affine threefolds. We also establish that…

We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$…

In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results…

Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset…

We investigate duality transformations in a class of backgrounds with non-Abelian isometries, i.e. Bianchi-type (homogeneous) cosmologies in arbitrary dimensions. Simple duality transformations for the metric and the antisymmetric tensor…

This paper proposes a new notion of smoothness of algebras, termed differential smoothness, that combines the existence of a top form in a differential calculus over an algebra together with a strong version of the Poincar\'e duality…

We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…

We extend the "bundle constructions" of calibrated submanifolds, due to Harvey--Lawson in the special Lagrangian case, and to Ionel--Karigiannis--Min-Oo in the cases of exceptional calibrations, by "twisting" the bundles by a special…

Pre-geodesics of an affine connection are the curves that are geodesics after a reparametrization (the analogous concept in K\"ahler geometry is known as J-planar curves). Similarly, dual-geodesics on a Riemannian manifold are curves along…

Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as the reduced membrane equation [17]. In this paper, we show that, conversely, axially symmetric closed genus…

Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…

We consider abstract inverse problems between infinite-dimensional Banach spaces. These inverse problems are typically nonlinear and ill-posed, making the inversion with limited and noisy measurements a delicate process. In this work, we…

We classify Lagrangian submanifolds of complex space forms, whose second fundamental form can be written in a certain way, depending on a real parameter. For some special values of this parameter, the resulting submanifolds are ideal in the…