Related papers: Essential Killing fields of parabolic geometries: …
For every p >= 5, we determine all Z_p-invariant nonsingular quartic surfaces in the three dimensional projective space over an algebraically closed field of characteristic zero. In some cases, we also determine their full projective…
Conformal Killing forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We show the existence of…
The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…
In this paper, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components by using the pinching and plumbing deformations.
We review the topological structure, sitting in any supergravity theory, which has been recently discovered in arXiv: 1801.04940. We describe how such a structure allows for a cohomological reformulation of the generalized Killing spinor…
In this paper, we want to give an exposition of our recent work on linear and nonlinear potential theory and their applications in conformal geometry. We use potential theory to study linear and quasilinear equations arising from conformal…
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…
This article describes an entirely algebraic construction for developing conformal geometries, which provide models for, among others, the Euclidean, spherical and hyperbolic geometries. On one hand, their relationship is usually shown…
A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways. The…
In the main part of this thesis, we present the foundations and initial results of the Spinorial Geometry formalism for solving Killing spinor equations. This method can be used for any supergravity theory, although we largely focus on D=11…
By providing a procedure to apply Hrushovski's amalgamation method to the setting of classes of infinite structures, we introduce the notion of \textit{paracollapsed} structures. We show that this approach provides existentially closed…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We present the most general curvature obstruction to the deformed parabolic orthosymplectic symmetry subalgebra of the supersymmetric quantum mechanical models recently developed to describe Lichnerowicz wave operators acting on arbitrary…
The second order Killing and conformal tensors are analyzed in terms of their spectral decomposition, and some properties of the eigenvalues and the eigenspaces are shown. When the tensor is of type I with only two different eigenvalues,…
We study groups definable in existentially closed geometric fields with commuting derivations. Our main result is that such a group can be definably embedded in a group interpretable in the underlying geometric field. Compared to earlier…
We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field…
We consider automorphisms of homogeneous parabolic geometries with a fixed point. Parabolic geometries carry the distinguished distributions and we study those automorphisms which enjoy natural actions on the distributions at the fixed…
The Killing tensors of arbitrary rank on complex projective space with its Fubini-Study metric are determined and it is shown that these spaces are generated by the Killing fields.
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
We study the intrinsic geometry of area minimizing (and also of almost minimizing) hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. For any such hypersurface we define and construct a so-called…