Related papers: On the Relationship between D'Angelo q-type and Ca…
We clarify the relationship between the two most standard measurements of the order of contact of q-dimensional complex varieties with a real hypersurface, the Catlin and D'Angelo $q$-types, by showing that the former equals the generic…
Notions of finite type play an important role in several complex variables. The most standard notion is D'Angelo type, which measures the order of contact of holomorphic curves with the boundary of a domain in ${\mathbb C}^n$. For the $\bar…
In [6], D'Angelo introduced the notion of finite type for points $p$ of a real hypersurface $M$ of $\mathbb C^n$ by defining the order of contact $\Delta_q(M,p)$ of complex analytic $q$-dimensional varieties with $M$ at $p$. Later, Catlin…
We consider an alternative approach to a fundamental CR invariant - the Catlin multitype. It is applied to a general smooth hypersurface in $\mathbbC^{n+1}$, not necessarily pseudoconvex. Using this approach, we prove biholomorphic…
Non-degenerate real hypersurfaces of almost Hermite-like manifolds are examined. Tangential real hypersurfaces are introduced and the main identities of such hypersurfaces are obtained. With the help of these identities, contact metric…
The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and…
We investigate real hypersurfaces in complex space forms attaining equality in an inequality involving the contact $\delta$-invariant $\delta^c(2)$ introduced by Chen and Mihai in [3].
The purpose of this paper is to investigate the geometric properties of real hypersurfaces of D'Angelo infinite type in ${\mathbb C}^n$. In order to understand the situation of flatness of these hypersurfaces, it is natural to ask whether…
We examine $q-$series related to higher forms. These forms are cubics, quartics, etc. In some points, in the article we add parts from previous works, in such a way, the article be more complete and readable.
We prove analogues of several well-known results concerning rational morphisms between quadrics for the class of so-called quasilinear $p$-hypersurfaces. These hypersurfaces are nowhere smooth over the base field, so many of the geometric…
We show the existence of elements of infinite order in some homotopy groups of the contactomorphism group of overtwisted spheres. It follows in particular that the contactomorphism group of some high dimensional overtwisted spheres is not…
We use high-precision spectroscopy and detailed theoretical modelling to determine the form of the coupling between a superconducting phase qubit and a two-level defect. Fitting the experimental data with our theoretical model allows us to…
The purpose of this paper is to investigate order of contact on real hypersurfaces in ${\mathbb C}^n$ by using Newton polyhedra which are important notion in the study of singularity theory. To be more precise, an equivalence condition for…
We provide a novel criterion for identifying quantum correlation, which allows us to find connections between Bell type inequalities, entanglement detection, and correlation. We utilize the criterion to construct witness operators that can…
While Q-balls have been investigated intensively for many years, another type of nontopological solutions, Q-tubes, have not been understood very well. In this paper we make a comparative study of Q-balls and Q-tubes. First, we investigate…
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
Correlations between electrons and the effective dimensionality are crucial factors that shape the properties of an interacting electron system. For example, the onsite Coulomb repulsion, U, may inhibit, or completely block the intersite…
We introduce a new class of models for interacting particles. Our construction is based on Jacobians for the radial coordinates on certain superspaces. The resulting models contain two parameters determining the strengths of the…
A contact hypersurface in a Kaehler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kaehler manifolds. We then…
In this article, we propose a q-analogue of the Drinfeld-Sokolov hierarchy of type A. We also discuss its relationship with the q-Painleve VI equation and the q-hypergeometric function.