相关论文: Canonical Cartan connection and holomorphic invari…
In the paper is we generalize known descriptions of rings of semi-invariants for regular modules over Euclidean and canonical algebras to arbitrary concealed-canonical algebras.
In every Engel manifold we construct an infinite family of pairwise non-isotopic transverse tori that are all smoothly isotopic. To distinguish the transverse tori in the family we introduce a homological invariant of transverse tori that…
In a recent paper, the author and I. Zelenko introduce the concept of modified CR symbols for organizing local invariants of $2$-nondegenerate CR structures. In this paper, we consider homogeneous hypersurfaces in $\mathbb{C}^4$, a natural…
We show that the extended principal bundle of a Cartan geometry of type $(A(m,\mathbb{R}),GL(m,\mathbb{R}))$, endowed with its extended connection $\hat\omega$, is isomorphic to the principal $A(m,\mathbb{R})$-bundle of affine frames…
In the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant…
We study regularity properties of CR maps in positive codimension valued in pseudoconvex manifolds which carry a nontrivial Levi foliation. We introduce an invariant which can be used to deduce that any sufficiently regular CR map from a…
We study a geometry associated with rank 3 distributions in dimension 8, whose symbol algebra is constant and has a simple Lie algebra sp(3,R) as Tanaka prolongation. We restrict our considerations to only those distributions that are…
Characteristic class relations in Dolbeault cohomology follow from the existence of a holomorphic geometric structure (for example, holomorphic conformal structures, holomorphic Engel distributions, holomorphic projective connections, and…
Recently there has been renewed interest among differential geometers in the theory of Engel structures. We introduce holomorphic analogues of these structures, and pose the problem of classifying projective manifolds admitting them.…
In this article the notion of ultradifferentiable CR manifold is introduced and an ultradifferentiable regularity result for finitely nondegenerate CR mappings is proven. Here ultradifferentiable means with respect to Denjoy-Carleman…
Representations of CCR algebras in spaces of entire functions are classified on the basis of isomorphisms between the Heisenberg CCR algebra A_H and star algebras of holomorphic operators. To each representations of such algebras,…
In this companion paper to our article {\em Accidental CR structures} (arxiv.org, January 2023), thought of as an appendix not submitted for publication, we provide complete explicit lists of infinitesimal CR automorphisms for the concerned…
We apply spectral sequences to derive both an obstruction to the existence of $n$-fold prolongations and a topological classification. Prolongations have been used in the literature in an attempt to prove that every Engel structure on…
We define a renormalized characteristic class for Einstein asymptotically complex hyperbolic (ACHE) manifolds of dimension 4: for any such manifold, the polynomial in the curvature associated to the characteristic class euler-3signature is…
We prove that there are no unexpected universal integral linear relations and congruences between Hodge, Betti and Chern numbers of compact complex manifolds and determine the linear combinations of such numbers which are bimeromorphic or…
We explore the different geometric structures that can be constructed from the class of pairs of 2nd order PDE's that satisfy the condition of a vanishing generalized W\"{u}nschmann invariant. This condition arises naturally from the…
We consider pairs of Lagrangian submanifolds $(L_0,L), (L_1, L)$ belonging to the class of Lagrangian submanifolds with \emph{conic} ends on \emph{Weinstein manifolds}. The main purpose of the present paper is to define a canonical chain…
We determine a 2-codimensional CR-structure on the slit tangent bundle $T_0M$ of a Finsler manifold $(M, F)$ by imposing a condition regarding the almost complex structure $\Psi$ associated to $F$ when restricted to the structural…
Motivated by recent works in Levi degenerate CR geometry, this article endeavours to study the wider and more flexible para-CR structures for which the constraint of invariancy under complex conjugation is relaxed. We consider…
We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the quiver variety. As a by-product, we give a counterexample…