Related papers: Quadratic differentials in spherical CR geometry
The purpose of this paper is to describe certain CR-covariant differential operators on a strictly pseudoconvex CR manifold $M$ as residues of the scattering operator for the Laplacian on an ambient complex K\"{a}hler manifold $X$ having…
We study the pseudohermitian sectional curvature of a CR manifold.
Modelled on a real hypersurface in a quaternionic manifold, we introduce a quaternionic analogue of CR structure, called quaternionic CR structure. We define the strong pseudoconvexity of this structure as well as the notion of quaternionic…
We study two kinds of curvature invariants of Riemannian manifold equip\-ped with a complex distribution $D$ (for example, a CR-submanifold of an almost Hermitian manifold) related to sets of pairwise orthogonal subspaces of the…
In this paper we introduce paraquaternionic CR-submanifolds of almost paraquaternionic hermitian manifolds and state some basic results on their differential geometry. We also study a class of semi-Riemannian submersions from…
This paper establishes the basis of the quaternionic differential geometry ($\mathbbm H$DG) initiated in a previous article. The usual concepts of curves and surfaces are generalized to quaternionic constraints, as well as the curvature and…
A helical CR structure is a decomposition of a real Euclidean space into an even-dimensional horizontal subspace and its orthogonal vertical complement, together with an almost complex structure on the horizontal space and a marked vector…
We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin$^{c, r}$ structure carrying a…
We characterize the subclass of quasianti-Hermitian quaternionic Hamiltonian dynamics such that their complex projections are one-parameter semigroup dynamics in the space of complex quasi-Hermitian density matrices. As an example, the…
We give a new CR invariant treatment of the bigraded Rumin complex and related cohomology groups via differential forms. A key benefit is the identification of balanced $A_\infty$-structures on the Rumin and bigraded Rumin complexes. We…
We develop the notion of renormalized energy in CR geometry, for maps from a strictly pseudoconvex pseudohermitian manifold to a Riemannian manifold. This energy is a CR invariant functional, whose critical points, which we call CR-harmonic…
Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…
We introduce pseudoconformal structures on 4--dimensional manifolds and study their properties. Such structures are arising from two different complex operators which agree in a 2--dimensional subbundle of the tangent bundle; this subbundle…
We compute a recently introduced geometric invariant of stricly pseudoconvex CR 3-manifolds for certain circle invariant spherical CR structures on Seifert manifolds. We give applications to the problem of filling the CR manifold by a…
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…
We construct a versal family of deformations of CR structures in five dimensions, using a differential complex closely related to the differential form complex introduced by Rumin for contact manifolds.
On real hypersurfaces in complex space forms many results are proven. In this paper we generalize some results concerning extrinsic geometry of real hypersurfaces, to CR submanifolds of maximal CR dimension in complex space forms.
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
The mathematics of a 4-dimensional renormalizable generally covariant lagrangian model (with first order derivatives) is reviewed. The lorentzian CR manifolds are totally real submanifolds of 4(complex)-dimensional complex manifolds…
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…